asked 177k views
2 votes
A piece of art is in the shape of a rectangular pyramid like the figure shown.

A rectangular pyramid with a base of dimensions 7 feet by 6 feet. The two large triangular faces have a height of 7.79 feet. The two small triangular faces have a height of 8 feet.

How much glass is needed to cover the entire pyramid?

1 Answer

1 vote

Answer:

144.53 square feet

Explanation:

You want the total surface area of a rectangular pyramid with base dimensions 7 ft by 6 ft and face slant heights of 7.79 ft and 8 ft.

Surface area

The surface area of the pyramid is the sum of the areas of the triangular faces and the area of the base.

Face area

The area of each triangular face is given by ...

A = 1/2bh

There are two faces of each dimension, so the lateral area will be ...

LA = (7 ft)(7.79 ft) +(6 ft)(8 ft) = 102.53 ft²

Base area

The base area will be the product of the rectangle dimensions:

B = LW

B = (7 ft)(6 ft) = 42 ft²

Total area

Then the total surface area is 102.53 ft² +42 ft² = 144.53 ft².

The area of glass needed to cover the entire pyramid is 144.53 ft².

__

Additional comment

The triangular face on the long side will have a shorter slant height, since the base of that triangle is closer to the center of the pyramid.

<95141404393>

answered
User Abhishek Honrao
by
7.4k points

No related questions found

Welcome to Qamnty — a place to ask, share, and grow together. Join our community and get real answers from real people.