Please answer this correctly

The quarter circle's area is 38.47 yard²

Step-by-step explanation:

The area of a full circle is pi * r ²

The area of a quarter circle is 1/4 * pi * r ²

Given:

Use 3.14 for pi

Round to the nearest hundredths.

Perimeter of quarter circle is 24.99 yards

For r you must leave it as 'r' because we do not know it for now...

1. Circumference of a full circle = 2* pi * r

2. 1/4 * ( 2 * pi * r )

1/4 * ( 2 * 3.14 * r )

1/2 * 3.14 * r

1.57 * r

3 Since r = 'r'

We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.

4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch

1.57 * r + 2 * r = 24.99

( 1.57 + 2 ) * r = 24.99

3.57 * r = 24.99

Divide left and right of the = sign by 3.57

3.57 / 3.57 * r = 24.99 / 3.57

1 * r = 24.99 / 3.57

r = 7

The area of a quarter circle is 1/4 * pi * r ²

1/4 * pi * 7²

1/4 * 49 * pi

49/4 * pi

49/4 * 3.14

38.465

Round to the nearest hundredths gives 38.47 yard²

The quarter circle's area is 38.47 yard²