Question

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

Answer 1

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.