Answer:
[tex]91\operatorname{cm}^2[/tex]
Explanation:
Step 1. The information that we have about the regular heptagon is:
The apothem, which we will call ''a'':
[tex]a=5.2cm[/tex]
The perimeter, which we will call ''P'':
[tex]P=35cm[/tex]
Step 2. The formula to find the area of any regular polygon (in this case a heptagon) is:
[tex]A=\frac{P\times a}{2}[/tex]
Where A is the area, P is the perimeter and a is the apothem.
Step 3. Substitute the values of P and a into the formula:
[tex]A=\frac{35cm\times5.2cm}{2}[/tex]
Solving the operations we find the area:
[tex]\begin{gathered} A=\frac{182cm^2}{2} \\ \\ A=\boxed{91\operatorname{cm}^2} \end{gathered}[/tex]
Answer:
[tex]91\operatorname{cm}^2[/tex]
