What is the total area of the plate glass that forms the base and lateral faces of the pyramid? Round your answer to the nearest whole number.

Question

You are making a regular square pyramid with a height of 14 centimeters and a base edge length of 8 centimeters using a base and lateral faces made of plate glass.

The total area of the plate glass is ____ square centimeters.

Answer 1

To do this we need to figure out the area of the square base which is 8x8 =64 and add it to the area of the 4 equal triangular faces so need to know the base and altitude of the trianglular face. Can form a right triangle using the height of the pyramid(14) and the distance from the center of the base to the edge(4) as legs and the altitude (A) as the hypotenuse

So (A)^2 = (4)^2 + (14)^2

A^2 = 16 + 196 = 212

A= 14.56

Area of the triangular face is (1/2) base x altitude = (1/2) x 8 x 14.56=58.24

There are 4 faces so 4 x 58.24 = 232.96

Total area is 232.96(area of 4 faces) + 64 (area of base) =296.96 cm^2