Question

7. The vertices of a rectangle 16 x 12 is on a circle.
The area of the circle is

please give the answer with explanation fast......​

Answer 1

______Answer ________

"An inscribed rectangle’s diagonal will be a diameter of the circle, so finding its length leads to the circle’s radius which is all we need."

The Diameter/diagonal is the hypotenuse of a right triangle with shorter sides of 5 and 12 units.

According to the Pythagorean Theorem, a^2 + b^2 = c^2

So 5^2 + 12^2 = D^2 ( Where “D” is our Diameter, hypotenuse, and diagonal.)

Therefore 25 + 144 = 169 = D^2

Taking the square root of both sides leaves

13 = D

Dividing the Diameter in half gives the circle a radius of 6.5 units.

So the circle’s area is pi * (6.5)^2 or pi * 42.25 units squared and the rectangle’s area is 5 units * 12 units which equals 60 units squared.

Using 3.14 as an approximation for pi becomes 3.14 * 42.25 = 132.665 units squared

Lastly we take that circle area and subtract the rectangle’s area from it for the final answer:

132.665 - 60 = 72.665 units squared (approximately)