The roof is in the shape of a square pyramid with a side length of 32 feet and a slant height of 20 feet. We need to find the total number of shingles required to cover the roof, given that 4 shingles cover 1 square foot. We need to round the final answer to the nearest whole number.

1. Problem Description

The roof is in the shape of a square pyramid with a side length of 32 feet and a slant height of 20 feet. We need to find the total number of shingles required to cover the roof, given that 4 shingles cover 1 square foot. We need to round the final answer to the nearest whole number.

2. Solution Steps

First, we need to find the lateral surface area of the square pyramid.

The lateral surface area of a square pyramid is given by the formula:

$Lateral Surface Area = 2 * side * slant\ height$

where $side$ is the length of the base of the square and $slant\ height$ is the height of the triangular face.

In this problem, $side = 32$ feet and $slant\ height = 20$ feet.

Therefore, the lateral surface area is:

$Lateral\ Surface\ Area = 2 * 32 * 20 = 1280\ square\ feet$

Since it takes 4 shingles to cover 1 square foot, the total number of shingles needed is:

$Total\ shingles = Lateral\ Surface\ Area * Shingles\ per\ square\ foot$

$Total\ shingles = 1280 * 4 = 5120$

Since we have a whole number already, we don't need to round.

3. Final Answer

5120