An artist used silver wire to make a square that has a perimeter of 40 inches. she then used copper wire to make the largest circle that could fit in the square, as shown below.

what is the area of the copper circle? use 3.14 to represent π.

The area of the copper circle A= 69.08 .

Step-by-step explanation:

Given data,

Perimeter of the Square =40 inches.

Let us find the measurement of one side.

The formula for perimeter of a square is 4a.

where a is length of one side of a square.

We know that perimeter of the square is 40.

∴ 4a=40.

a=10 inches.

Imagine that moving one side of the square into the circle.

You can observe that length of one side of square is the diameter of the circle.

∴Diameter of the circle =10 inches.

⇒ Radius of the circle r= 5 inches.

Area of the circle A= π.

A= 3.14×5×5.

Area of the circle A= 69.08 .

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.