Question

A barn is shaped like a rectangular prism with a triangular prism on top as shown. The exterior four walls and two triangular faces need to be repainted. If one gallon of paint covers 232 square feet, how many gallons will it take to repaint the barn? Enter your answer in the box. AlternativeText

Answer 1

Image used in answering the question is attached below.

Answer: 21.97gallons

Step-by-step explanation:

Calculating the total area to be painted :

The exterior four walls :

The exterior walls have rectangular front, back and two sides.

Area of rectangular front and back :

Length(L) = 32ft

Width(W) = 20ft

Area of rectangle = L × W

32 × 20 = 640ft^2

Front and back = 640ft^2 × 2 = 1280ft^2

Area of rectangular sides :

Length = 84

Width = 20

2 × (84 × 20) = 3360ft^2

Area of triangular front and back :

Area of triangle = (0.5) × base × height

Base = 38ft, height = 12ft

(0.5) × 38 × 12 = 228ft^2

Two triangles = 2 × 228 = 456ft^2

Total area to be painted :

(456 + 3360 + 1280)ft^2 = 5096ft^2

Gallons required = total area to be painted / area covered by one gallon

5096ft^2/232ft^2 = 21.965gallons

Answer 2

21.975 gallons will take to repaint the barn.

How to elaborate the problem ?

Given that, Length of each of front & back exterior walls is 32 ft.

Width of each of front & back exterior walls is 20 ft.

Length of each of side exterior walls is 84 ft.

Width of each of side exterior walls is 20 ft.

Base of a triangular prism is 38 ft. & height is 12 ft.

How to find quantity of paint required ?

First, we have to find area of each of rectangular front & back walls.

Area = Length × Width = (32×20) sq. ft. = 640 sq. ft.

Total area of front & back wall = (2×640) sq. ft. = 1280 sq. ft.

Now, we have to find the area of each of rectangular side walls,

Area = Length × Width = (84×20) sq. ft. = 1680 sq. ft.

Total area of two side walls = (2×1680) sq. ft. = 3360 sq. ft.

Area of one triangular side = $\frac{1}{2}$×base×height

                                               = ($\frac{1}{2}$×38×12) sq. ft.

                                               = 228 sq. ft.

Area of two triangular sides = (2 × 228) sq. ft. = 456 sq. ft.

∴ The total area to be painted = (456+3360+1280) sq. ft. = 5096 sq. ft.

Paint required = Total area to be painted/area covered by one gallon

                        = 5096/232 gallons

                        = 21.965 gallons

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