Question

Find the area of the regular octagon if the apothem is 4.2 and a side is 3.4 In. Round to the nearest whole number. A. 114 B. 57 C. 157 D. 94

Answer 1

B.
`57\text{ in}^2`

Explanation:

We have been that apothem of a regular octagon is 4.2 inches and length of each side is 3.4 inches. We are asked to find the area of our given octagon.

We know that area of octagon is half the product of perimeter and apothem of the octagon.

`\text{Area of octagon}=(1)/(2)* (a\cdot p)`, where,

a = Apothem of octagon,

p = perimeter of octagon.

We will find perimeter of our given octagon by multiplying length of each side by 8.

`\text{Perimeter of octagon}=8* 3.4\text{ in}`

`\text{Perimeter of octagon}=27.2\text{ in}`

`\text{Area of octagon}=(1)/(2)* (4.2\text{ in}\cdot 27.2\text{ in})`

`\text{Area of octagon}=(1)/(2)* (114.24\text{ in}^2)`

`\text{Area of octagon}=57.12\text{ in}^2\approx 57\text{ in}^2`

Therefore, the area of our given octagon is 57 square inches and option B is the correct choice.

Answer 2

The area of the regular octagon is calculated as half of the product of the perimeter and the apothem (ap), using the formula of the area of the regular polygon.
We have then:
A = ((p) * (ap)) / 2
Where,
p: perimeter
ap: apotema
Substituting values:
A = ((8 * 3.4) * (4.2)) / 2
A = 57.12 in ^ 2
Answer:
the area of the regular octagon is:
B. 57