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? $\frac{9}{16}$, $\frac{3}{4}$, $\frac{4}{3}$, $\frac{16}{9}$

Explanation:

Step1: Recall the area - side length relationship

For similar figures, if the ratio of corresponding side lengths is $k$, the ratio of their areas is $k^{2}$. Here, the ratio of the side length of the smaller pyramid to the side length of the larger pyramid is $k=\frac{3}{4}$.

Step2: Calculate the ratio of the base - areas

The base of a square - pyramid is a square. The ratio of the base area of the smaller pyramid to the base area of the larger pyramid is $k^{2}$. Substitute $k = \frac{3}{4}$ into $k^{2}$, we get $(\frac{3}{4})^{2}=\frac{3^{2}}{4^{2}}=\frac{9}{16}$.

Answer:

$\frac{9}{16}$