Question

An artist creates two metal sculptures in the shape of regular octagons a side of the larger octagon is 3.5 times longer than a side of the smaller octagon the area of the smaller octagon is 19.28 square inches

Answer 1

The area of the larger octagon is
`236.18\ in^2`

Explanation:

The question is

What is the area of the larger octagon?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

so

Let

z ----> the scale factor

x ----> the area of the larger octagon

y ---> the area of the smaller octagon

`z^2=(x)/(y)`

we have that

`z=3.5`

Because, in similar figures the ratio of corresponding sides is proportional and this ratio is equal to the scale factor

we have

`z=3.5`

`y=19.28\ in^2`

substitute the given values

`3.5^2=(x)/(19.28)`

`x=12.25(19.28)=236.18\ in^2`