Question

I keep putting in the formula but I keep getting the answer wrong​

Answer 1

Answer:

314 in²  (nearest whole number)

Step-by-step explanation:

Radius of a regular polygon: The distance from the center of the polygon to any vertex.  The radius of a hexagon is equal to the length of one side.

Therefore, from inspection of the given diagram:

• radius = 11 in  ⇒  side length = 11 in

To find the area of a regular polygon, we first need to calculate the apothem.   The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.

$\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}$

where:

• s = length of one side
• n = number of sides

Given:

• s = 11 in
• n = 6

Substitute the given values into the formula and solve for a:

$\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}$

Area of a Regular Polygon

$\textsf{A}=\dfrac{n\:s\:a}{2}$

where:

• n = number of sides
• s = length of one side
• a = apothem

Given:

• n = 6
• s = 11

• $\textsf{a}=\dfrac{11\sqrt{3}}{2}$

Substitute the given values into the formula and solve for A:

$\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}$

$\implies \sf A=314.3672216...$

$\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)$