Question

The scale factor of two similar hexagons is 5:12. The smaller hexagon has an area of 24 square units. What is the area of the larger hexagon?

Answer 1

Answer: $138.24\ \text{square units}$

Step-by-step explanation:

Given

The scale factor of two similar hexagons is 5:12.

The smaller hexagon has an area of 24 square units

we know, the ratio of two similar figures is equal to the square of the scale factor.

Suppose the area of the larger hexagon is A

$\therefore \dfrac{24}{A}=\left[\dfrac{5}{12}\right]^2\\\\\Rightarrow A=\left[\dfrac{12}{5}\right]^2\times 24\\\\\Rightarrow A=138.24\ \text{square units}$