Answer:
a. In the given figure,
The triangular prism is placed above a cuboid,
[tex]\because \sqrt{4^2+10^2}=\sqrt{16+100}=\sqrt{116}[/tex]
∴ Surface area of the triangular prism,
[tex]A_1= 2\times \frac{1}{2}\times 20\times 4+2\times \sqrt{116}\times 45[/tex]
[tex]=(80 + 90\sqrt{116})\text{ square feet}[/tex]
Now, the surface of the cuboid having dimensions 20' × 45' × 15'
So, the surface area of the cuboid,
[tex]A_2=2\times 20\times 15 + 2\times 45\times 15[/tex]
[tex]=1950\text{ square feet}[/tex]
Hence, the total surface area of the house,
[tex]A=A_1+A_2[/tex]
[tex]=80+90\sqrt{116}+1950[/tex]
[tex]=2999.32966528[/tex]
[tex]\approx 2999.33\text{ square feet}[/tex]
b. ∵ 1 paint = 57 square feet,
⇒ 1 square feet = [tex]\frac{1}{57}[/tex] paints,
⇒ The number of cans required for 2999.33 square feet = [tex]\frac{2999.33}{57}[/tex] ≈ 53
c. Since, the cost of one can = $ 23.50,
So, the cost of 53 cans = $ 1245.5,
d. The volume inside the barn = Volume of triangular prism + volume of cuboid
= 1/2 × 20 × 4 × 45 + 20 × 45 × 15
= 15,300 cube feet.
