Question

Find the perimeter and area of the regular polygon. Round to the nearest tenth

Answer 1

Answer: perimeter = 24

Area = 41.6

Step-by-step explanation:

The polygon show in the diagram is a hexagon. It has six sides, since it is a regular hexagon, all the six sides are equal.

From the information given, the apotherm = 2√3

The formula for determining the area of the polygon is expressed as

Area of polygon

=area = a^2n ×tan 180/n

Therefore,

Area = (2√3)^2 × 6 × tan(180/6)

Area = (2√3)^2 × 6 × tan 30

Area = 12 × 6 × 0.5774

Area = 41.6

The formula for determining the perimeter of a polygon is

Area = pa/2

Where

P represents the perimeter of the polygon.

a represents the apotherm of the polygon. Therefore

41.6 = p × 2√3/2

p = 41.6/√3

p = 24

Answer 2

Answer:

P = 24

A ≈ 41.6

Step-by-step explanation:

The polygon is a regular hexagon, so the triangle shown is a 30-60-90 triangle.  So the short leg of the triangle is 2, which makes the side length of the hexagon 4.

That means the perimeter is P = 4 × 6 = 24.

The area of a regular polygon is:

A = ½ aP

where a is the apothem and P is the perimeter.

A = ½ (2√3) (24)

A = 24√3

A ≈ 41.6