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

`(b* h)/(2)`

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

`a* b\text{.}`

Structure VI is a semicircle, so the area is

`(\pi r^2)/(2)\text{.}`

All the areas are in squared feet.

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

`(10*11)/(2)=55`

Structure II (a=37, b-10)

`37*10=370`

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

`26*24=624`

Structure IV (a=32, b=9)

`32*9=288`

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

`(9*8)/(2)=36`

Structure VI (r=12)

`((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.