What is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm? Round your answer to the nearest hundredth

Answer 1

To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.

1. The area of the base:
Since the base is a square, we can use the formula for the area of a square: A = side^2.
The base edge is given as 1.5 cm, so the area of the base is 1.5^2 = 2.25 cm^2.

2. The area of the four triangular faces:
Each triangular face is a right triangle. We can use the formula for the area of a right triangle: A = 0.5 * base * height.
The base of each triangular face is the same as the base edge of the square pyramid, 1.5 cm.
The height of each triangular face is given as the slant height, which is 4 cm.
So, the area of each triangular face is 0.5 * 1.5 * 4 = 3.00 cm^2.
Since there are four triangular faces, the total area of the four faces is 4 * 3.00 = 12.00 cm^2.

Therefore, the surface area of the square pyramid is the sum of the base area and the area of the four faces:
Surface area = Base area + 4 * Face area
Surface area = 2.25 + 12.00 = 14.25 cm^2

Rounded to the nearest hundredth, the surface area is 14.25 cm^2.