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
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
[tex]\begin{gathered} \frac{200}{A}=\frac{25}{16} \\ A=200\cdot\frac{16}{25} \\ =128\text{ cm}^2 \end{gathered}[/tex]The area of the smaller hexagon is 128 square centimetres.
Final Answer: The area of the smaller hexagon is 128 square centimetres.
