Area Composite Figures

Area - Simulation

Area - How it Works - Video

Example 1a

Example 1a:

For composite figures, the first step is find the missing lengths so that we find the area of the two rectangles. Sometimes we get lucky and we don't need to. We will understand when we need to do that after practice. The two missing side lengths are the two red lines. The main characteristic that we need to remember is that opposite side of rectangles are equal. So 4 cm + ____ = 11 cm. The missing side length is 7 cm. The other missing side length can be found by using, 7 cm + ____ = 10 cm. The missing side length is 3 cm.

Now that we have found the missing side lengths we can separate the composite figure into 2 rectangles. Let's use the area formula, which is Area = Length times Width. Area of orange rectangle = 10 cm times 4 cm = 40 cm². Area of white rectangle = 7 cm times 3 cm = 21 cm². Now we have to add the two rectangles to find our composite figure. The result is 61 cm² because 40 cm² plus 21 cm² = 61 cm².

Example 1b

Example 1b:

We are using the same figure, but we have cut the composite figure the other way.

Let's use the area formula, which is Area = Length times Width. Area of orange rectangle = 7 cm times 4 cm = 28 cm². Area of white rectangle = 11 cm times 3 cm = 33 cm². Now we have to add the two rectangles to find our composite figure. The result is 61 cm² because 28 cm² plus 33 cm² = 61 cm².

It doesn't matter which way we cut the composite into two shapes, the result will be the same.

Example 2a

Example 2a:

For composite figures, the first step is find the missing lengths so that we find the area of the two rectangles. Sometimes we get lucky and we don't need to. We will understand when we need to do that after practice. The two missing side lengths are the two red lines. The main characteristic that we need to remember is that opposite side of rectangles are equal. So 3 cm + ____ = 7 cm. The missing side length is 4 cm. The other missing side length can be found by using, 2 cm + 6 cm = ____. The missing side length is 8 cm.

Now that we have found the missing side lengths we can separate the composite figure into 2 rectangles. Let's use the area formula, which is Area = Length times Width. Area of orange rectangle = 4 cm times 2 cm = 8 cm². Area of white rectangle = 8 cm times 3 cm = 24 cm². Now we have to add the two rectangles to find our composite figure. The result is 32 cm² because 8 cm² plus 24 cm² = 32 cm².

Example 2b

Example 2b:

We are using the same figure, but we have cut the composite figure the other way.

Let's use the area formula, which is Area = Length times Width. Area of orange rectangle = 7 cm times 2 cm = 14 cm². Area of white rectangle = 6 cm times 3 cm = 18 cm². Now we have to add the two rectangles to find our composite figure. The result is 32 cm² because 14 cm² plus 18 cm² = 32 cm^2.

It doesn't matter which way we cut the composite into two shapes, the result will be the same.

Example 3a

Example 3a:

This time we are going to find the area of the composite figure a little bit differently. If we take a look at the green rectangle, it is comprised of the orange, white, and dark green rectangles. So if we find the area green and subtract the area of the dark green rectangle, we will find the area of the original composite (orange and white). So the Area of the green = 12 cm times 10 cm = 120 cm². Now we must find the area of the dark green one. Area of the dark green = 7 cm times 6 cm = 42 cm². The result of subtracting the two rectangles is 78 cm² because 120 cm² minus 42 cm² = 78 cm².

Take a look at 3b if you prefer the other method.

Example 3b

Example 3b:

For composite figures, the first step is find the missing lengths so that we find the area of the two rectangles. Sometimes we get lucky and we don't need to. We will understand when we need to do that after practice. This time if we take the time and separate the composite the right way, then we don't need to find the missing side lengths.

Let's use the area formula, which is Area = Length times Width. Area of orange rectangle = 12 cm times 4 cm = 48 cm². Area of white rectangle = 6 cm times 5 cm = 30 cm². Now we have to add the two rectangles to find our composite figure. The result is 78 cm² because 48 cm² plus 30 cm² = 78 cm².

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