Question

rectangles abcd and efgh are similar. the length of each side of efgh is 6 times the length of the corresponding side of abcd. the area of abcd is 66 square units. what is the area, in square units, of efgh?
a 11
b 36
c 396
d 2,376

Explanation:

Step1: Recall the ratio - area relationship for similar figures

For two similar figures, if the ratio of the corresponding side lengths is \(k\), the ratio of their areas is \(k^{2}\). Here, the ratio of the side - length of \(EFGH\) to the side - length of \(ABCD\) is \(k = 6\).

Step2: Calculate the area of \(EFGH\)

Let the area of \(ABCD\) be \(A_1=66\) square units and the area of \(EFGH\) be \(A_2\). Since \(\frac{A_2}{A_1}=k^{2}\), and \(k = 6\), then \(A_2=k^{2}\times A_1\). Substitute \(k = 6\) and \(A_1 = 66\) into the formula: \(A_2=6^{2}\times66=36\times66 = 2376\) square units.

Answer:

D. 2,376