Question

A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 50 feet and the slant height of each lateral side of the pyramid is 40 feet.

A painter can paint 100 square feet of the pyramid in 18 minutes.

How long does it take the painter to paint 75% of the pyramid?

Enter your answer, rounded to the nearest tenth, in the box.

Answer 1

Explanation:

The lateral surface area of the pyramid can be found using the formula for the area of an equilateral triangle:

A = (s^2 * √3) / 4

where s is the length of one side of the equilateral triangle base.

For this pyramid, s = 50 feet

A = (50^2 * √3) / 4 = (2500 * √3) / 4 = 1250 * √3 ≈ 2129.28 ft^2

The total surface area of the pyramid can be found by adding the area of the base to the area of the lateral surface:

A = base area + lateral surface area

A = (side length^2 * √3) / 4 + (3 * triangle area)

A = (50^2 * √3) / 4 + (3 * (50^2 * √3) / 4)

A = 2500 * √3 + 3750 * √3 ≈ 5884.28 ft^2

To paint 75% of the pyramid, the painter needs to paint 75% * 5884.28 ft^2 = 4413.71 ft^2

Since the painter can paint 100 ft^2 in 18 minutes, he can paint 4413.71 ft^2 in 4413.71 / 100 * 18 minutes ≈ 786.96667 minutes

Rounding to the nearest tenth, the painter will take 786.967 minutes to paint 75% of the pyramid, which is approximately 13.1 hours.