How do we discover the location of composite figures?

In this lesson we’ll look at composite figures made from rectangles and also how to discover their locations.

You are watching: How to find the area of a composite figure

A compowebsite figure is made by combining different forms. We’ll uncover the location of a compowebsite figure by separating the compowebsite shape into shapes whose locations we already know how to discover.


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Area making use of a sum

Let’s look at the compowebsite figure listed below, which is made of rectangles. We have the right to divide the shape into 2 rectangles, use the location formula for a rectangle twice to uncover their individual locations, and then include their areas to obtain the full location of the figure.


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A form can be divided in even more than one way, but no issue how we divide the shape, the worth of the location will always be the very same. We can divide this figure into two rectangles through a horizontal line.


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The height of the whole figure is ???12???, and also the elevation of the top rectangle is ???5???, so we have the right to discover the elevation of the reduced rectangle by subtraction: ???12-5=7???. Now we recognize the dimensions of both of the smaller rectangles.

The dimensions of the top rectangle are???12??? and also ???5???, so its location is

???A=bh???

???A=(12 ext ft)(5 ext ft)???

???A=60 extft^2???

The dimensions of the reduced rectangle are???4??? and also ???7???, so its location is

???A=bh???

???A=(4 ext ft)(7 ext ft)???

???A=28 extft^2???

So the full area of the figure is

???A=60+28???

???A=88 extft^2???

We might additionally divide this figure right into 2 rectangles with a vertical line.


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The length of the entire figure is ???12???, and the size of the appropriate rectangle is ???4???, so we deserve to discover the length of the left rectangle by subtraction: ???12-4=8???. Now we understand the dimensions of both rectangles.

The dimensions of the left rectangle are???8??? and ???5???, so its area is

???A=lw???

???A=(8 ext ft)(5 ext ft)???

???A=40 extft^2???

The dimensions of the right rectangle are???4??? and also ???12???, so its location is

???A=lw???

???A=(4 ext ft)(12 ext ft)???

???A=48 extft^2???

So the full area of the number is

???A=40+48???

???A=88 extft^2???

Area making use of a difference

You have the right to additionally use a distinction to find the area of a composite number. Let’s look at this one again.


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The base of the brand-new, big rectangle we created is ???12???, so the base of the rectangle we drew to fill in the empty space should be ???12-4=8???. The elevation of the new, big rectangle we created is ???12???, so the height of the rectangle we drew to fill in the empty room must be ???12-5=7???.

The area of the brand-new, big rectangle we created (which is actually a square since its base is equal to its height) is ???12cdot 12=144 extft^2???. The area of the rectangle we attracted to fill in the empty room is ???7cdot 8=56 extft^2???. So to discover the location of the original number, we deserve to subtract the area of the rectangle we attracted to fill in the empty room from the location of the brand-new, huge rectangle we formed:

???A=144-56=88 extft^2???

Which is the exact same area we got as soon as we offered sums of areas of two rectangles instead of a distinction of locations of 2 rectangles. Let’s perform some even more examples.

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How to uncover the location of compowebsite numbers using sums and differences


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Finding the location of figures made by combining rectangles

Example

The number is made by combining rectangles. What is the location of the figure?


The height of the reduced rectangle is ???2???, so we can discover the elevation of the top rectangle by subtracting ???4-2=2???cm. The dimensions of the top rectangle are ???5??? by ???2???, so its area is

???A=bh???

???A=5cdot 2???

???A=10 extcm^2???

We need to include to uncover the base of the reduced rectangle. Its base is made of the horizontal ???6??? cm and the horizontal ???5??? cm. So the base of the reduced rectangle is ???6+5=11??? cm. The dimensions of the lower rectangle are therefore ???2??? by ???11???, so its area is

???A=bh???

???A=2cdot 11???

???A=22 extcm^2???

So the total location of the figure is

???A=10+22=32 extcm^2???


A shape deserve to be separated in even more than one means, but no matter exactly how we divide the form, the worth of the area will certainly constantly be the very same.


The elevation of the whole number is ???8???, and the base of the totality figure is ???15???. The dimensions of the whole figure are ???15??? by ???8???, so its location is

???A=bh???

???A=15cdot 8???

???A=120 extcm^2???

The empty room has a height of ???3???, and we can discover the base by subtracting ???15-5=10??? cm. The dimensions of the empty room are therefore ???10??? by ???3???, so its location is

???A=bh???

???A=10cdot 3???

???A=30 extcm^2???

We deserve to then say that the area of the original figure is

???A=bh???

???A=120-30???

???A=90 extcm^2???


Discover mathKrista KingJanuary 31, 2021math, learn digital, digital course, digital math, geomeattempt, location and also perimeter, area of a rectangle, rectangular area, sums and distinctions, compowebsite figures
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