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