Question

A regular heptagon has an apothem of approximately 6.7 cm and a perimeter of approximately 45.5 cm.

Find the area of the heptagon.

Answer 1

304.85 cm²

Explanation:

The area (A) of a polygon is calculated as

A = pa ( p is the perimeter and a the apothem ) , thus

A = 45.5 × 6.7 = 304.85 cm²

Answer 2

The area of the regular heptagon is approximately 152.225 square centimeters.

How to solve for the area of the heptagon

The formula to calculate the area of a regular polygon when given the apothem and perimeter is:

`\[ \text{Area} = (1)/(2) * \text{Apothem} * \text{Perimeter} \]`

For a regular heptagon (a seven-sided polygon) with an apothem of approximately 6.7 cm and a perimeter of approximately 45.5 cm:

`\[ \text{Area} = (1)/(2) * 6.7 \, \text{cm} * 45.5 \, \text{cm} \]\[ \text{Area} = (1)/(2) * 6.7 * 45.5 \, \text{cm}^2 \]\[ \text{Area} = 152.225 \, \text{cm}^2 \]`

Therefore, the area of the regular heptagon is approximately 152.225 square centimeters.