Question

Find the surface area of the pyramid. The side lengths of the base are equal. Square pyramid with base edge of 7 inches, and a slant height measuring 5 inches, on a triangular face.

Answer 1

To find the surface area of the pyramid, first find the area of the base and the area of the triangular faces. The base is a square pyramid, and its area is the side length squared. The triangular faces can be found using the area of a triangle formula.

Step-by-step explanation:

To find the surface area of the pyramid, we need to find the area of the base and the area of the four triangular faces. Since the base is a square pyramid, the area of the base is the side length squared, which is 7 inches squared. The area of each triangular face can be found using the formula for the area of a triangle: 1/2 times the base times the height.

The base of the triangle is the side length of the base, which is 7 inches, and the height is the slant height, which is 5 inches. Therefore, the area of each triangular face is (1/2) * 7 inches * 5 inches.

There are four triangular faces, so the total area of the triangular faces is 4 times (1/2) * 7 inches * 5 inches. The total surface area of the pyramid is the sum of the area of the base and the area of the triangular faces. Therefore, the surface area of the pyramid is 7 inches squared + 4 times (1/2) * 7 inches * 5 inches.

Answer 2

Surface area of the square based pyramid is 134.4in²

Step-by-step explanation:

Surface area of the square based pyramid is expressed as:

S = a²+2a√a²/4 + h²

a is the base edge

h is the slant height of the pyramid

Given a = 7in, h = 5in

S = 7²+2(7)√7²/4+5²

S = 49+ 14√49/4+25

S= 49+ 14√149/4

S = 49+14√37.25

S = 49+14(6.1)

S = 49+85.4

S = 134.4in²