# A rectangle whose dimensions are 12 in. and 15 in. is circumscribed about a circle. What is the circumference of the circle? What is the area outside the rectangle but inside the circle?

1
by Jnnll

• Brainly User
2016-01-09T23:13:09+08:00
Find the diagonal of the rectangle using Pythagorean Theorem:

Diagonal
=
=
=
= 3   or 3(6.40)
= 19.2 inches

Solve for Circumference:
C = 2 π r

Radius (r)of circumscribing circle of rectangle:
= diagonal ÷ 2
= 19.2 inches ÷ 2
= 9.6 inches

Circumference = 2 (3.14) (9.6 inches)
= 60.23 inches

ANSWER: CIRCUMFERENCE of circle = 60.23 inches

Area of Circumscribing circle:
= π r²
= (3.14) (9.6 inches)²
= (3.14) (92.16 inches²)
= 289.38 inches²

Area of rectangle:
= Length × Width
= 15 inches × 12 inches
= 180 inches²

Area outside the rectangle but inside the circumscribing circle:
= Area of circle - area of rectangle
= 289.38 inches² - 180 inches²
= 109.38 inches²

ANSWER: 109.38 inches² is the area outside the rectangle but within the circumscribing circle.