Question

Find the area of each regular polygon below. Round values to the nearest 0.01. Show work for all steps clearly.

Answer 1

The area of the hexagon and pentagon area 779.4cm^2 and 84.303cm^2 respectively.

Data;

• apothem = 15

Area of a Hexagon

The area of a hexagon with apothem 15 can be calculated by first finding the length of the side of the hexagon.

Length of hexagon can be found using trigonometric ratio;

$a = x\sqrt{3}$

Making x the subject of formula

$x = \frac{a}{\sqrt{3} }\\x = \frac{15}{\sqrt{3} }\\x = 8.660$

And then the length of the side is 2x

$s = 2 * 8660 = 17.32$

The perimeter of the hexagon is;

$p = 6s \\p = 6 * 17.32=103.92$

And the area is given as

$A = \frac{1}{2} * perimeter * apothem\\A = \frac{1}{2} * 103.92 * 15\\A = 779.4unit^2$

The area of the hexagon is 779.4 squared unit.

Area of the pentagon

The area of the pentagon can be found using several methods, but we can simply find the angle between the sides if we divide the pentagon into 10 pieces and then substitute the formula.

Total area of a pentagon is 360 degree.

$\theta = \frac{360}{10} = 36^0$

The area of a pentagon is given as

$A = \frac{5s^2}{4 tan \theta} \\A = \frac{5 * 7^2}{4* tan36} \\A = 84.303cm^2$

The area of the pentagon is 84.303cm^2

From the calculations above, the area of the hexagon and pentagon area 779.4cm^2 and 84.303cm^2 respectively

Learn more on area of polygons here;

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