Question

6. Here is an octagon.

3 in
4 in 3 in
→
3 in
a. While estimating the area of the octagon, Lin
reasoned that it must be less than 100 square
inches. Do you agree? Explain your reasoning.
b. Find the exact area of the octagon. Show your
reasoning.
4 in
3 in

Answer 1

a). Yes. Area will be less than 100 square in.

b). Area of octagon = 82 in²

Explanation:

From the picture attached,

a). Octagon is inscribed in a square having one side = 10 inches.

Since, octagon is obtained by cutting off the four equal corners of the square,

Area of octagon will be less than the area of the square.

Area of square = (side)²

= 10²

= 100 in²

Therefore, area of octagon will be less than 100 in²

b). Since, corner cut off from the square are equal in shape and area,

Area of one corner (right angle triangle) =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(3)(3)`

= 4.5 in²

Area of 4 corners = 4.5 × 4 = 18 in²

Area of octagon = Area of square - Area of 4 corners removed

= 100 - 18

= 82 in²