Question

the two square pyramids are similar. the side length of the smaller pyramid is $\frac{3}{4}$ the side length of the larger pyramid. which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger pyramid? 20 m 15 m $\frac{9}{16}$ $\frac{3}{4}$ $\frac{4}{3}$ $\frac{16}{9}$

Explanation:

Step1: Recall the ratio - area relationship for similar figures

For two similar figures, if the ratio of their corresponding side - lengths is \(a:b\), the ratio of their areas is \(a^{2}:b^{2}\). Here, the ratio of the side - length of the smaller pyramid to the side - length of the larger pyramid is \(\frac{3}{4}\).

Step2: Calculate the ratio of the base areas

Let \(a = 3\) and \(b = 4\). The ratio of the base area of the smaller pyramid to the base area of the larger pyramid is \(\frac{a^{2}}{b^{2}}=\frac{3^{2}}{4^{2}}=\frac{9}{16}\).

Answer:

A. \(\frac{9}{16}\)