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.