Question

Find the area of the smaller octagon that has a side length of 15 feet

Answer 1

Question

An octagon has a side length of 18 feet and an area of 806.4 ft^2

Find the area of a smaller octagon that has a side length of 15 feet

Answer:

Explanation:

We are given two octagons in the above question.

Side length of larger octagon = 18 feet

Area of larger octagon = 806.4 ft^2

The area of a smaller octagon = X

Side length of smaller octagon = 15 feet

We solve for this using scale factor

Scale factor(k) = ratio of the side length of the octagon = smaller side length/ larger side length

k = 15/18

It is important to note that

The square of the scale factor k = ratio of the areas of the octagon

Hence,

`k^2=(x)/(806.4)`
`((15)/(18))^2=(x)/(806.4)`
`(15^2)/(18^2)=(x)/(806.4)`

Cross Multiply

`x=806.4\cdot(15^2)/(18^2)`

x = 560 ft^2