Question

You need to paint the three rectangular sides of the right triangular prism below. How much paint do you need to cover all the rectangular faces of the prism?

A prism which has a right triangle for the base and a height of 12 inches. The legs of the right triangle are 5 inches and 12 inches.

A. 300 in²
B. 360 in²
C. 204 in²
D. 420 in²

Answer 1

To solve this problem, one must find the surface area of the rectangles. This is the total area of each rectangle added together. The formula for the area of the rectangle is w*l=A

Rectangle one: 13*12 = 156 in^2

Rectangle two: 5*12 = 60 in^2

Rectangle three: 12*12 = 144 in^2

156 + 60 + 144 = 360 in^2

This means total to paint the rectangle sides of the prism, we need 360 in^2 of paint.

Answer 2

B. 360 in²

Explanation:

Rectangle 1

length = 12 in

breadth = 12 in

Surface area = length × breadth

⇒Surface area = 12 × 12

⇒Surface area = 144 inch²

Rectangle 3 (behind)

length = 12 in

breadth = 13 in

Surface area = length × breadth

⇒Surface area = 12 × 13

⇒Surface area = 156 inch²

Rectangle 2

length = 12 in

breadth = 5 in

Surface area = length × breadth

⇒Surface area = 12 × 5

⇒Surface area = 60 inch²

Adding the 3 areas we get

144+156+60 = 360 in²

∴ 360 in² of paint is needed to cover all the rectangular faces of the prism.