Question

A building has the shape of a pyramid within a square base. The mid segment parallel to the ground of each triangular face of the pyramid has a length of 58 feet. Find the length of the base the pyramid.

Answer 1

The length of the base the pyramid is 116 feet.

Explanation:

See the diagram attached to this answer.

Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.

Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.

Hence,
`(OA')/(OA) = (OB')/(OB) = (A'B')/(AB) = (1)/(2)`

⇒ AB = 2 × 58 = 116 feet.

The length of the base the pyramid is 116 feet. (Answer)