The 2972 square feet of surface area that Shane will paint, if he will paint the 4 rectangular sides, 2 triangular pieces and he will not paint the rectangular sections of roof.
Step-by-step explanation:
The given is,
Shane wants to paint,
4 rectangular sides
2 triangular sides
Step:1
From the given diagram,
Total surface area of paint = (4 Rectangular sides surface ares) +
(2 triangular sides surface area)....(1)
Step:2
Surface area of 4 rectangular sides,
For Left side(rectangle) surface area,
[tex]A =lb[/tex]...........................................................(2)
From the given diagram.
= (45.5 × 20)
= 910 Square feet
Dimensions of left side and right side are equal, so area of right side equal to the left side.
Area of right side = 910 square feet
Area of left and right sides,
= Left side area+ Right side area
= 910 + 910
= 1820 square feet
For front side area,
[tex]A =lb[/tex]...........................................................(3)
From the given diagram,
= (24 × 20 )
= 480 square feet
Dimensions of front side and back sides are equal, so area of front side equal to the back side.
Area of front side = 480 square feet
Area of front and back sides,
= front side area+ back side area
= 480 + 480
= 960 square feet
Surface area of rectangular sides,
= Area of left and right sides + Area of front and back sides
= 1820 + 960 = 2780 square feet
Step:3
Surface area of 2 triangular faces,
For area of triangular sides,
[tex]A = \frac{hb}{2}[/tex]...............................................(4)
From the given values,
= [tex]\frac{(8)(24)}{2}[/tex]
= [tex]\frac{192}{2}[/tex]
= 96 square feet
Dimensions of front side triangle and back side triangles are equal, so area of front side triangle equal to the back side triangle.
Area of front side triangle = 96 square meters
Area of front and back side triangles,
= front side triangle area+ back side triangle area
= 96 + 96
= 192 square feet
Step:4
From the equation (1),
Total surface area of paint = 2780 + 192
Total surface area of paint = 2972 square feet
Result:
The 2972 square feet of surface area that Shane will paint, if he will paint the 4 rectangular sides, 2 triangular pieces and he will not paint the rectangular sections of roof.
