Exercise 40 Page 648

We want to find the area of a regular polygon with a perimeter of 54m, and apothem of 3sqrt(3)m. To do so, let's recall that the area of a regular polygon is half the product of the apothem and the perimeter. A= 12ap Since we already know the measures for the apothem and the perimeter, we can substitute these values in the formula to find the area.

A=1/2ap

Substitute

a= 3sqrt(3),p= 54

A= 1/2( 3sqrt(3))(54)

▼

Evaluate right-hand side

CommutativePropMult

Commutative Property of Multiplication

A= 1/2(54)(3sqrt(3))

MoveRightFacToNumOne

1/b* a = a/b

A= 54/2(3sqrt(3))

CalcQuot

Calculate quotient

A= 27(3sqrt(3))

Multiply

Multiply

A= 81sqrt(3)

UseCalc

Use a calculator

A= 140.296115...

RoundDec

Round to 1 decimal place(s)

A≈ 140.3

The area of the regular polygon rounded to the nearest tenth is 140.3m^2.