Question

A regular polygon has 7 sides it has a side length of 10 cm what is the area of the polygon? The apothem is about 11.26 cm

Answer 1

To find the area of a regular polygon, you can use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]

For a regular polygon with \( n \) sides, the perimeter can be calculated as:

\[
\text{Perimeter} = n \times \text{side length}
\]

In this case, for a regular polygon with \( n = 7 \) sides and a side length of \( 10 \) cm:

\[
\text{Perimeter} = 7 \times 10 \, \text{cm} = 70 \, \text{cm}
\]

Now, substituting the values into the area formula:

Given that the apothem is approximately \( 11.26 \) cm, we can now calculate the area:

\[
\text{Area} = \frac{1}{2} \times 70 \, \text{cm} \times 11.26 \, \text{cm}
\]
\[
\text{Area} = \frac{1}{2} \times 70 \times 11.26
\]
\[
\text{Area} = 35 \times 11.26
\]
\[
\text{Area} \approx 394.1 \, \text{cm}^2
\]

Thus, the area of the regular heptagon (7-sided polygon) with a side length of 10 cm and an apothem of approximately 11.26 cm is about \( 394.1 \, \text{cm}^2 \).