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Article Summary

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It’s easiest to find the area of a regular pentagon if you know the length of a side and the apothem. The apothem is a line that intersects one of the sides from the center of the pentagon at a 90° angle. For example, let’s say you have a pentagon with a side length of 3 units and an apothem of 2 units. You can now divide the pentagon into 5 triangles, each with a base width of 3 (equal to the length of one side of the pentagon) and a height of 2 (equal to the apothem). To find the area of the pentagon, all you need to do is find the area of one of the triangles and multiply the result by 5. Use the formula ½ x base x height to find the area of each triangle. In this example, ½ x 3 x 2 = 3, so each triangle has an area of 3 square units. Multiply 3 x 5 to get 15 square units, or the area of the entire pentagon. You can also use the formula Area = Pa/2, where P is the perimeter of the pentagon and a is the apothem. In the example above, the perimeter would be 3 x 5 = 15, and the apothem is 2. (15 x 2)/2 = 30/2, which is equal to 15. If you only know the side length of the pentagon, you can still figure out the area, but you’ll need to do a bit of trigonometry. Start by dividing the pentagon into 5 equal triangles, starting from a point at the center of the pentagon. The base of each triangle will be equal to the length of a side of the pentagon. Now, divide one of the triangles in half by drawing a vertical line from the vertex to the middle of the base to create two right triangles. You know that the base of the smaller triangle is ½ of the side length of the pentagon. So, if you have a pentagon with a side length of 7 units, the base of the smaller right triangle is 3.5 units. When you’re working with a regular pentagon, the angle at the top of this triangle will always be 36°. To find the height of the triangle, use the formula tan36° = b (base)/h (height) and solve for h. In our example, tan36° = 3.5/h. Multiply tan36° by h, then divide 3.5 by tan36° to find the height, which is approximately 4.8 units. Now you can plug the height into the formula for the area of a triangle, 1/2 x b x h, to find the area of the triangle. Plug in the base of the larger triangle for the b variable and the height you just found for the h variable to get ½ x 7 x 4.8 = 16.8 square units. Then, multiply the area of the larger triangle by 5 to get the full area of the pentagon, or 84 square units. Alternatively, you can plug the base width of the smaller triangle into the formula for the area of a triangle, then multiply the result by 10. Either way, you’ll get the same answer. You can also calculate the area from only the side length using the formula 5s2/4tan36°, where s is the length of one side of the pentagon. If you don’t have a calculator with a tangent function, don’t worry. Tan36° = √(5-2√5), so you can plug that into your calculations in place of tan36°. You can also figure out the area of a pentagon using only the radius, or r, which is the distance from the center of the pentagon to one of the corners, or vertices. To do this, use the formula 5/2 x r^2 x sin72°. For more on finding the area of a regular pentagon, including using formulas if you only know the length of a side or the radius, read on!

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2 Ways To Change The Color Of A Layer In Procreate

All you need to do to change the color of a layer in Procreate is to drag and drop your desired color directly onto the layer. Ensure the layer you want to recolor is the active layer. Then drag the color wheel in the top right corner and drop it onto your canvas.

I’m Carolyn and I set up my own digital illustration business over three years ago. Since then, I have been using Procreate to create digital artwork on the app almost every single day of my life so I am well-versed with every shortcut that Procreate has to offer.

This drag-and-drop tool allows you to quickly change the color of not only layers but individual shapes too. This is not one of the first things I learned on Procreate but I really wish it was as it is a serious time saver. Today I’ll show you how to use this simple and quick method.

Key Takeaways

There are two ways to change the color of a layer in Procreate.

You can also change the color of a specific shape or section of your layer.

Dropping a color on different shades of a pattern or layer will provide you with different results in color.

2 Ways to Change the Color of a Layer in Procreate

There are two ways to change the color of a layer in Procreate. Open your iPad and follow the step by step below. I will start by showing you the most basic method for covering your full layer in one color. 

Method 1: Color Wheel

Step 1: Ensure the layer you want to change the color of is the active layer. You can do this by simply tapping on the layer and you will notice the layer is highlighted in blue once it is active.

Step 2: Once you have chosen the color you want to use it will be active in your color wheel in the top right-hand corner of your canvas. Drag and drop it onto the layer.

Step 3: This color will now fill your entire layer. At this point, you can either undo or repeat steps 1 and 2 with a different color until you are satisfied with the result.

Method 2: Hue, Saturation, Brightness

This next method is more time-consuming but can give you more control over your color choice without having to drag and drop your color wheel multiple times.

Step 1: Ensure the layer you want to change the color of is active. In the top left-hand corner of your canvas, tap on the Adjustments tool (magic wand icon). Choose the first option in the drop-down labeled Hue, Saturation, Brightness.

Step 2: A toolbox will appear at the bottom of your canvas. Here you can manually adjust the hue, saturation, and brightness of your entire layer. Adjust each tab until you are happy with the results.

How to Change the Color of a Shape – Step by Step

Maybe you don’t want to color the entire layer, just a specific shape or part of a layer. Here’s how:

Step 1: Ensure the shape you want to change the color of is Alpha Locked. This will ensure that only your selected shape is filled rather than the whole layer it is on.

Step 2: Once you have chosen the color you want to use it will be active in your color wheel in the top right-hand corner of your canvas. Drag and drop it onto the shape.

Step 3: The shape will now fill with whatever color you have dropped onto it. 

Note: You can also use Method 2 shown above to change the color of a specific shape or selection.

Pro Tip: When you drag and drop color onto a layer with multiple shades of color, it will change the color of the layer differently depending on which shade you drop your color on. 

See my example below. When I drop the same color blue onto the light or dark part of my pattern, it will give me two different results.

FAQs

Below I have answered a small selection of your frequently asked questions regarding changing the color of a layer in Procreate:

Can I recolor one item in Procreate?

Yes, you can. Use the method shown above. Ensure your shape is on Alpha Lock and drag and drop your desired color directly onto your shape.

How to change the color of lines on Procreate?

You can use both Methods 1 & 2 listed above to do this. You will need to zoom in on your canvas to ensure that you can drop your color wheel within the line you want to recolor.

How to change the text color in Procreate?

You can change the color of your text while you’re still adding it to your canvas. Or you can use both Methods 1 & 2 shown above to do this if you’re too far gone from the Edit Text stage.

How to darken a layer in Procreate?

Follow Method 2 shown above but only adjust the Brightness toggle at the bottom of the toolbox. Here you can change the darkness of your color without it affecting the hue or saturation of it.

How to change the color of the pen in Procreate?

Tap on the color wheel in the top right-hand corner of your canvas. Once it opens the full-color wheel, drag your finger over the colors until you find the one you want to use. This will now activate your pen color in Procreate and you’re ready to draw.

Conclusion

As I mentioned before, this was not one of the first things I learned to do on Procreate but I wish I did. It saves so much time and also gives you the ability to explore your color wheel to its full extent. This is a great way to learn your color theory on the Procreate app.

If you haven’t already, I highly recommend adding this skill to your Procreate repertoire if you want to really up your drawing game. This will absolutely save you time in the long run and I wish I learned it sooner. Don’t make the same mistakes that I did!

3 Ways To Remove The Background From An Image On Mac

Do you have a photo where you’d like to keep the main focus, the subject, but remove the rest? You don’t need a third-party photo editor to do this on macOS. Instead, we’ll show you built-in ways to remove the background from an image on Mac.

You can remove the background in your photo using the Photos app, a Finder Quick Action, or the Preview app. Each method has limitations, so check them out and see which will work best for you.

Table of Contents

Use Photos to Remove an Image Background

Introduced with macOS Ventura, you can remove the background of an image and then paste the remaining portion where you like. For instance, you can pop it into an email or text message.

You’ll then see your image pasted without its background.

The nice thing about this method is that you can remove an image background without effort and keep the original photo intact. However, you do have to paste the image somewhere, which may not always be ideal.

Use Finder to Remove an Image Background

Another update with macOS Ventura was the addition of a Quick Action in Finder to remove a photo background.

Pick

Remove Background

in the menu.

If you don’t see this option, choose

Customize

at the bottom of the Quick Actions list.

Then, check the box for

Remove Background

and select

Done

. You’ll then see the action in the Quick Actions list.

Once you select the

Remove Background

Quick Action, you’ll see a new image created in the same folder with only the subject and no background.

This method gives you another fast way to remove an image background. The only downside is that it’s not always exact. For example, you may miss part of the subject in the final product, such as a dog’s tail or a girl’s ponytail.

Use Preview to Remove an Image Background

If you want to be more precise when you remove image backgrounds, you can use the Preview app. Here are two different ways to do this in Preview.

Trace the Subject

This first method allows you to trace the portion you want to keep and remove the rest using the Smart Lasso tool.

Open your image in Preview and choose

Markup

in the toolbar.

Select the drop-down arrow for the

Selection Tools

button and pick

Smart Lasso

.

Draw around the part of the picture you want to keep. You’ll see a broad red line as you do so, letting you capture all of those small things you don’t want to leave out.

To complete the border, connect your ending line to the beginning line.

If you’re using a JPG image, you’ll be asked to convert it to a PNG file format to complete the process. Select

Convert

to continue.

You’ll then have your image without a background.

Remove Areas by Color

If you have a photo where the subject has distinct colors from the background, you can use the Instant Alpha tool in Preview.

Open your image in Preview and choose

Markup

in the toolbar.

Select the

Instant Alpha

button (magic wand) in the toolbar.

Drag your cursor over part of the background area. Preview selects that section and any adjacent areas with the same colors.

When you release the cursor, these then display with a highlighted or glowing border.

Use your

Delete

key to remove the selected area.

Like the above method, you’ll be asked to convert the image to a PNG if you’re using a JPG file format.

Continue this process until all of the image’s background is removed.

Perfect Your Pictures

When you need to get rid of a photo bomber, blurred background, or unwanted distraction behind the main focus, you can easily remove the background from an image on Mac with these options.

Let us know which one you decide to use or if you use different photo editing methods depending on the image.

For related tutorials, look at ways to make an image transparent on Mac and Windows.

3 Ways To Fix The Browser Not Supported Error In Lacerte

3 Ways to Fix the Browser Not Supported Error in Lacerte Apply these fixes to fix Lacerte not supported by the browser problem

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Lacerte is a powerful taxing software developed by Intuit that helps professionals in the seamless tax filing process.

Some users have reported that they aren’t able to access Intuit-related websites on their browsers.

This guide lists some solutions that have helped users fix the problem at their end.

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You deserve a better browser! Over 300 million people use Opera One daily, a fully-fledged navigation experience coming with various built-in packages, enhanced resource consumption, and great design.

Here’s what Opera One can do:

Optimize resource usage: Opera One uses your Ram more efficiently than Brave

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Lacerte Tax is a cloud-based online professional tax software offering from Intuit. Using this tool, you can accurately prepare business and individual returns with any level of complexity. In addition, Lacerte Tax comes with the benefit of preparing returns securely from anywhere on any device.

While the tool is useful, some users reported facing a browser not supported for the Lacerte issue.

If you are also experiencing a browser not supported Lacerte issue and are looking for solutions, you have landed in the right place.

This guide will give you some of the best solutions that have helped users resolve the browser not supported in Lacerte error. So let us get right into it.

Why am I having issues when visiting Intuit websites?

If you are trying to visit any of the Intuit websites and come across an error that says Our systems are experiencing some issues. Please try again later, or browser not supported error, then there can be many reasons for this problem.

This could be because of the corrupt cache and data of the browser.

Intuit isn’t added as a trusted website.

There is some issue with the browser settings.

These reasons may be general, but the browser not supported for Lacerte error is a widespread problem caused by common issues.

In the next section, we will discuss the solutions that will help you fix the problem at your end.

Quick Tip:

Lacerte’s cloud-based taxing software is compatible with any Chromium-based browser. Opera One works excellently since it utilizes your default applications option for the web browser to open the hyperlink. 

Furthermore, moving to Opera One is simple since you will be prompted to transfer all saved information from your existing browser. This way, nothing is lost, but every other benefit is won.

Opera One

Switch to this flexible browser, and just deal with taxes without errors.

Free Visit Website

Is Lacerte compatible with Windows 11?

Expert tip:

How can I fix Lacerte browser not supported error? 1. Clear browser cache

We have explained the steps for the Google Chrome browser since it is the most commonly used web browser by millions across the globe.

However, if you use a different browser, you can follow similar steps or check the official forums for help.

Often, corrupted cache and browser files can cause multiple issues within the browser and prevent you from using it optimally. However, you can try clearing the browser cache and data and check if this fixes the browser not supported Lacerte issue or not.

2. Add Intuit as a trusted site

The above is just one of the ways you can add trusted websites on your PC for the web browsers. You can check out the other ways of adding a website as a trusted site in Chrome on Windows 10/11 & Mac. Adding a website as a Trusted Site will bypass the high security of your PC only after you have permitted it.

If the website isn’t set as a trusted site, you could encounter issues such as the browser not supporting Lacerte or Intuit not supporting this browser error. Add the Intuit website as a trusted site and check if this fixes the problem at hand or not.

3. Reset the browser

There are chances that some of the extensions that you have installed on your browser might have changed the browser settings, due to which you are coming across the Lacerte not supported in browser error.

Apart from disabling all the extensions, you can try resetting the browser using the above steps.

If the above solutions do not work, your browser could be an issue. You can try updating it from the About section of the browser or switching to a different browser.

Now, since a good variety of web browsers are available, you might get confused about which one to go for. In such a scenario, we suggest you check out our guide on the best browsers you can use in 2023.

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How To Find The Row

> M1

Output      [,1] [,2] [,3] [,4] [,5] [1,]  2    2    1    2   2 [2,]  2    2    2    2   1 [3,]  2    2    1    1   1 [4,]  2    1    1    1   1 > M2 Output      [,1] [,2] [,3] [,4] [,5] [1,]  1    1    2    2    1 [2,]  2    1    1    2    1 [3,]  2    2    1    1    1 [4,]  2    1    1    2    2 [5,]  2    1    1    2    2 [6,]  1    2    1    1    2 [7,]  1    1    2    1    2 [8,]  2    2    1    2    1 [9,]  2    1    1    2    2 [10,] 1    1    2    2    2 [11,] 1    1    2    1    2 [12,] 1    2    2    2    1 [13,] 2    2    2    2    1 [14,] 2    1    2    2    1 [15,] 1    2    1    1    2 [16,] 2    2    1    2    1 [17,] 2    2    1    1    1 [18,] 2    1    1    2    1 [19,] 1    1    1    2    1 > M3 Output      [,1] [,2] [,3] [,4] [,5] [1,]  1    3    3    2    1 [2,]  2    3    1    2    2 [3,]  2    2    3    3    1 [4,]  1    3    1    3    2 [5,]  3    1    2    1    2 [6,]  2    3    1    1    1 [7,]  2    2    2    3    1 [8,]  1    2    2    2    2 [9,]  2    1    2    1    2 [10,] 1    3    1    2    1 [11,] 2    1    3    1    1 [12,] 1    1    3    2    2 [13,] 2    1    1    1    2 [14,] 2    1    3    3    2 [15,] 1    2    3    1    2 [16,] 1    2    1    2    1 [17,] 3    1    1    3    2 [18,] 3    3    3    3    1 [19,] 3    2    3    1    1 > M4 Output       [,1] [,2] [,3] [,4] [,5] [1,]  10    10   9    10   9 [2,]  9     9    10   9    9 [3,]  9     9    9    10   10 [4,]  10    9    9    10   10 [5,]  10    10   9    10   9 [6,]  10    10   9    10   10 [7,]  9     9    9    10   9 [8,]  9     10   9    10   9 [9,]  9     9    9    9    9 [10,] 9     10   9    10   9 [11,] 10    10   9    9    9 [12,] 9     9    9    9    9 [13,] 10    10   10   9 10 [14,] 10    9    10   10 10 [15,] 9     10   9    10 9 [16,] 9     10   9    10 9 [17,] 9     10   10   9 10 [18,] 9     9    9    9 10 [19,] 10    9    9    10 9

C++ Program To Find The Product Of Two Numbers Using Recursion

Recursion is a technique where we call a function from the same function itself. There must be some base or terminating condition to end the recursive call. Recursive procedures are very much helpful to perform complex iterative solution with fewer codes and easier solution approach through sub-operation finding.

In this article we shall discuss a recursive approach to perform product (multiplication) between two numbers in C++. Initially we will understand the basic principle, the syntax for recursive function call, the algorithm and the source code.

Multiplication using Recursion

In high-level languages, there is the multiplication operators available to directly perform multiplication. However we know that the multiplication is actually a repetitive addition. So the result of A * B is repetitive addition of A, B number of times, or we can say repetitive addition of B, A number of times. Whenever there is a repetition, we can do this using recursion. Let us see the recursive function definition syntax first.

Syntax

if ( base condition ) { terminate recursive call } recursive function call: function_name ( updated parameter list ) }

define a function multiply() which takes two numbers A and B

if A < B, then

return multiply( B, A )

otherwise when B is not 0, then

return A + multiply( A, B – 1 )

otherwise

return 0

end if

end of function definition

Read two inputs A and B

res = multiply( A, B )

display res

Example

using

namespace

std

;

int

multiply

(

int

A

,

int

B

)

{

if

(

A

<

B

)

{

return

multiply

(

B

,

A

)

;

}

else

if

(

B

!=

0

)

{

return

A

+

multiply

(

A

,

B

1

)

;

}

else

{

return

0

;

}

}

int

main

(

)

{

cout

<<

“Multiplication of 5, 7 is: “

<<

multiply

(

5

,

7

)

<<

endl

;

cout

<<

“Multiplication of 8, 0 is: “

<<

multiply

(

8

,

0

)

<<

endl

;

cout

<<

“Multiplication of 25, 3 is: “

<<

multiply

(

25

,

3

)

<<

endl

;

cout

<<

“Multiplication of 9, 1 is: “

<<

multiply

(

9

,

1

)

<<

endl

;

}

Output Multiplication of 5, 7 is: 35 Multiplication of 8, 0 is: 0 Multiplication of 25, 3 is: 75 Multiplication of 9, 1 is: 9

See, in this program, the function is taking parameters A and B both are two integer numbers. Now after each step it reduces the second parameter B by 1 and adding A with A itself. Like this the function is performing multiplication procedure.

Conclusion

Recursion is a process to call the same function from the function itself. While calling a function recursively, we update or change the parameter set a little so that the same effect is not coming again and again, then it divides the problem into smaller subproblems and solve the problem by solving these smaller problems in a bottom-up manner. Almost anything which can be implemented using loops, can also be implemented using recursion. In this article we have seen simple process to multiply two integers using recursion. The integers are added multiple times to get the final multiplication result.

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