Answer:
[tex]230 ft^2[/tex]
Step-by-step explanation:
Given : Carlos needs to paint the outside of the shed in his backyard, including its roof but not including its floor.
To Find: What is the total area of the surfaces that he needs to paint?
Solution:
Length of backyard= 8 feet
Breadth of backyard = 5 feet
Height of backyard = 6 feet
So, Area of walls of backyard = Lateral surface area = [tex]2(l+b) \times h[/tex]
= [tex]2(8+5) \times 6[/tex]
= [tex]156 ft^2[/tex]
Area of two triangular faces of roof = [tex]\frac{1}{2} \times Base \times Height \times 2[/tex]
Base of triangular face = 8 feet
Height of triangular face = 3 feet
So, Area of two triangular faces of roof = [tex]\frac{1}{2} \times 8 \times 3 \times 2[/tex]
= [tex]24 ft^2[/tex]
Area of two square roof = [tex]2 \times Side^2[/tex]
Side of square = 5 feet
So, Area of two square roof = [tex]2 \times 5^2[/tex]
= [tex]50ft^2[/tex]
So, total area to be painted = [tex]156 ft^2+24 ft^2+50ft^2[/tex]
= [tex]230 ft^2[/tex]
Hence the total area of the surfaces that he needs to paint is [tex]230 ft^2[/tex]
