Question

I need help with this now. She said that we were supposed to solve for the area of the composite structures inside the structures.

Answer 1

We can decompose the figure in structures such that we can calculate the area of each structure.

Then, we have 3 rectangles, two triangles and a semicircle. The semicircle has diameter equals to

$\begin{gathered} d=43ft-10ft-9ft=24ft \\ \end{gathered}$

Then, the radius is equal to r=12ft.

We divide the figure in 6 different structures:

Structures I and V are triangles, so their area is

$\frac{b\times h}{2}$

Structures II, III and IV are rectangles, so their area is

$a\times b\text{.}$

Structure VI is a semicircle, so the area is

$\frac{\pi r^2}{2}\text{.}$

All the areas are in squared feet.

Structure I (b=10, h=48-37=11)

$\frac{10\times11}{2}=55$

Structure II (a=37, b-10)

$37\times10=370$

Structure III (a=38-12=26, b=43-10-9=24)

$26\times24=624$

Structure IV (a=32, b=9)

$32\times9=288$

Structure V (b=9, h=40-32=8)

$\frac{9\times8}{2}=36$

Structure VI (r=12)

$\frac{(3.14)(12)^2}{2}=226.08$

Then, we can obtain the total area adding all the area of the structures.

$55+370+624+288+36+226.08=1599.08$

So, the total area is 1599.08 squared feet.