# Compound Shapes: How to Find the Area of an L-Shape

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Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.

## Finding the Area of a Compound Shape

A compound shape is a shape that is made up of other simple shapes. In this article, we will be working out the area of an L shape (made up of two rectangles). To find the area of a compound shape, follow these simple steps:

Step 1: Work out the missing lengths around the edge of the compound shape.

Step 2: Divide your L shape into two rectangles. This can be done in 2 different ways (both methods will give the same answer).

Step 3: Work out the area of each rectangle. Do this by multiplying the base of the rectangle by the height of the rectangle.

Step 4: Add the areas of the rectangles together to give the total area of the L shape.

Example 1

Find the area of this compound shape (L shape).

Step 1

Work out the missing lengths around the edge of the compound shape.

10 – 6 = 4 cm

9 – 2 = 7 cm

Step 2

Divide your L shape into two rectangles.

Scroll to Continue

In this case, I have put the line horizontally.

Step 3

Now you need to find the area of the 2 rectangles:

The area of rectangle A is 10 × 2 = 20 cm²

The area of rectangle B is 4 × 7 = 28 cm²

Make sure you select the correct base and height lengths for each rectangle.

Step 4

All you need to do now is to add up the 2 answers from step 3.

20 + 28 = 48 cm².

So the total area of the compound shape is 48 cm².

Summary:

Find the missing lengths around your L shape and divide the shape into 2 rectangles. Find the area of both rectangles and add them up to give the total area of the compound shape.

Question: How do you work out the volume of a prism from calculating the area of an L shape?

Answer: Once you have calculated the cross-sectional area of the prism, multiply the answer by the length of the prism.

So for example, if the cross-sectional area of the L shape was 50 cm^2 and the length 3cm, then the volume of the L shape would be 150 cm^3 (50 multiplied by 3).

Question: How do you know which measurements you are meant to multiply to find the area of a complex shape?

Answer: You multiply the two side lengths of each rectangle together (Base multiplied by Height).

Question: How do you find the area of a frame?

Answer: Work out the area of the inner and outer rectangles, and then find the difference between these area.

Assuming that the frame is rectangular.

Question: How do you know you have to put the line horizontal not vertical when finding the area of an L-shape?

Answer: You can split the compound shape up either way.

Both ways will result in the correct area.

Question: How do you know which sides to multiply on the L shape?

Answer: It must be the length and width of the rectangle (these are the two side lengths which make the rectangle).

Question: What if I need to find the area of something that is not L-shaped?

Answer: Other shapes can be split into rectangles too. T and H shapes are also common exam questions.

Question: How do you know where to draw the line in order to have two rectangles?

Answer: It can be horizontal or vertical, as long as it makes two rectangles.

Question: How do you know which numbers to add and which numbers to subtract when finding the area of an L-shape?

Answer: If the length your finding is longer than the two other sides then add them, if not subtract them.

Question: How do I find the perimeter of an L shape?

Answer: Once you have worked out all of the sides lengths, then you can add all these up to give the perimeter of the L shape.

Question: Is it only an L shape that can be used for compound shape?

Answer: No, it can be other shapes too, such as a T shape, or a H shape.

Question: How do you calculate perimeter?

Answer: The perimeter can be found by adding up all the side lengths around the L shape.

Question: How do you find the area if the shape has a half circle conected to it?

Answer: I think you mean a shape which can be split into a rectangle (or square) and a semi-circle.

Work out the area of the rectangle using length times width, and work out the area of the semi-circle using 0.5 times Pi times radius squared. Then add these two answers together.

Question: What does finding the area of the smaller shapes of an L shape help with?

Answer: Area helps you work out the space inside a shape.

It can be useful in real life for working out how much carpet you need to fit a floor space, or how much gravel you need to fill a garden.

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matt on July 05, 2013:

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