Question

4. The lengths of the shortest sides of two similar hexagons are 10 cm and 8 cm. Given that the areaof the larger hexagon is 200 cm?, find the area of the smaller hexagon.

Answer 1

Given:

Shortest side length of the larger hexagon = 10 cm

Shortest side length of the smaller hexagon = 8 cm

Area of the larger hexagon = 200 square centimeter

Required: Area of the smaller hexagon

Step-by-step explanation:

Use the fact that the area of any similar polygons are proportional to the square of the two corresponding sides.

The ratio of the shortest sides of hexagon is 10:8 or 5:4. Therefore, their areas are in the ratio 25/16.

Let A be the area of the smaller hexagon. Then

`\begin{gathered} (200)/(A)=(25)/(16) \\ A=200\cdot(16)/(25) \\ =128\text{ cm}^2 \end{gathered}`

The area of the smaller hexagon is 128 square centimetres.

Final Answer: The area of the smaller hexagon is 128 square centimetres.