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

Answer:

The length of the base the pyramid is 116 feet.

Step-by-step 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, $\frac{OA'}{OA} = \frac{OB'}{OB} = \frac{A'B'}{AB} = \frac{1}{2}$

⇒ AB = 2 × 58 = 116 feet.

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