Exercise 44 Page 352

The area of the octagon is the difference of the area of the rectangle and the four triangles.

Area of the Rectangle

Since the length and width of the rectangle is given, we can use the area formula A=l w to find the area of the rectangle.

A_(rectangle)=l w

SubstituteII

l= 30, w= 20

A_(rectangle)=( 30)( 20)

Multiply

Multiply

A_(rectangle)=600

Area of a Triangle

The length of the legs of the right triangle Barrington cut off is also given on the figure. We can use the area formula A= 12bh to find the area of the triangles.

A_(triangle)= 12bh

SubstituteII

b= 6, h= 6

A_(triangle)= 12( 6)( 6)

Multiply

Multiply

A_(triangle)=18

Area of the Octagon

Since the four triangles are congruent, their area is the same. We can find the area of the octagon by subtracting four times the area of the triangle from the area of the rectangle.

A_(octagon)=A_(rectangle)-4A_(triangle)

SubstituteII

A_(rectangle)= 600, A_(triangle)= 18

A_(octagon)= 600-4( 18)

Multiply

Multiply

A_(octagon)=600-72

SubTerms

Subtract terms

A_(octagon)=528

The area of the octagon is 528cm^2, so the correct answer choice is B.