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Find the Area of the following composite figure:O 43 square inchesO 84 square inchesO 31,500 square inchesO 150 square inches

Find the Area of the following composite figure:O 43 square inchesO 84 square inchesO-example-1
User Geoff Maddock
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1 Answer

13 votes
13 votes

So we have:

To find the area of the entire figure we can simply find the areas of each individual subfigure.

For rectangle A we have that its area is given by:


S_A=5in\cdot10in=50in^2

For rectangle B:


S_B=7in\cdot x

Where side x is given by:


\begin{gathered} x+6in=10in \\ x=10in-6in=4in \end{gathered}

Then the surface of rectangle B is:


S_B=7in\cdot4in=28in^2

C is a triangle, the area of a triangle is given by its base (y) times its height (x) divided by two:


S_C=(x\cdot y)/(2)=(4in\cdot y)/(2)

We need to find y using the length of the base of the total figure:


\begin{gathered} 15in=7in+5in+y=12in+y \\ y=15in-12in=3in \end{gathered}

Now that we found y we can find the area of the triangle:


S_C=(4in\cdot y)/(2)=(4in\cdot3in)/(2)=6in^2

The total area is then:


S_A+S_B+S_C=50in^2+28in^2+6in^2=84in^2

So the total area is 84 square inches.

Find the Area of the following composite figure:O 43 square inchesO 84 square inchesO-example-1
User Trosendal
by
3.0k points