Question

The surface area of a triangular pyramid is 400 square meters. The surface area of a similar triangular pyramid is 25 square meters. What is the ratio of corresponding dimensions of the smaller pyramid to the larger pyramid?

Answer 1

Explanation:

The ratio of corresponding dimensions of the smaller pyramid to the larger pyramid can be obtained by taking the square root of the ratio of their surface areas.

Let's call the corresponding dimensions of the smaller and larger pyramids h (height) and k (some other dimension, such as base edge or slant height), respectively.

Then, using the formula for the surface area of a triangular pyramid, we can write the given ratios as:

hₛᵣ / h = √(25/400) = 1/4

kₛᵣ / k = √(25/400) = 1/4

Therefore, the ratio of corresponding dimensions of the smaller pyramid to the larger pyramid is 1/4.