Question

1. in the diagram, ghjk ~ lmnp. find the area of lmnp.

area of ghjk = 84 m²

Explanation:

Step1: Find the scale factor

The corresponding sides of the similar rectangles are 7 m (for GHJK) and 21 m (for LMNP). The scale factor \( k \) is \( \frac{21}{7}=3 \).

Step2: Recall the area ratio of similar figures

For similar figures, the ratio of their areas is the square of the scale factor. Let \( A_1 \) be the area of GHJK and \( A_2 \) be the area of LMNP. Then \( \frac{A_2}{A_1}=k^2 \).

Step3: Calculate the area of LMNP

We know \( A_1 = 84 \, m^2 \) and \( k = 3 \), so \( k^2 = 9 \). Then \( A_2 = A_1\times k^2 = 84\times9 = 756 \, m^2 \).

Answer:

The area of \( LMNP \) is \( 756 \, m^2 \).