Give the area of a regular octagon with a side length of 7 inches and an apothem of 9.4

Answer 1

draw a diagram and divide the regular octagon into 8 congruent triangles

find the area of one triangle and multiply this area by 8

the apothem is the altitude and the side length is the base

A=(1/2)(7)(9.4)

A=32.9 inches

now multiply this answer by 8 because there are 8 triangles

A=8*32.9

A=263.2 sq inches

However, there is an easier way to get the answer.

If you found the area of each triangle, you would be using 1/2 eight times, the apothem, 9.4, eight times and the side length, 7, eight times.

If you use the side length, 7, eight times you are finding the perimeter of the octagon.

So, it's much easier to find the perimeter of the polygon and multiply the perimeter by the apothem (altitude), and then multiply the product by 1/2 or divide the product by 2.

Area=(1/2) * apothem * perimeter

A=(1/2)(9.4)(56) (8 times the side length of 7 gives 56)

A-(1/2)(526.4)

A=263.2 sq inches

Answer 2

Area of an octagon = 8(side length)(apothem)/2

Area = 8(7)(9.4)/2

Area = 263.2 in²