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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?

Sagot :

Find the diagonal of the rectangle using Pythagorean Theorem:

Diagonal = [tex] \sqrt{(15) ^{2}+(12) ^{2} } [/tex]
               = [tex] \sqrt{225 + 144} [/tex]
               = [tex] \sqrt{369} [/tex]
               = [tex] \sqrt{9(41)} [/tex]
               = 3 [tex] \sqrt{41} [/tex]  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.

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