Use Area of Circles to Solve Problems

PICTURE FRAMES The rectangular matting for a picture frame has a circular cutout for the photograph, as shown in the figure. What is the area of the mat? Round to the nearest tenth.

Use Area of Circles to Solve Problems

Answer: The area is about 165.7 sq. in.

Find the area of the rectangle minus the area of the circle.

Area of rectangle Area of circle

A = ℓw – r 2

= 18 ● 12 – ● 42 Replace ℓ with 18, w with12, and r with 4.

= 216 – 16 Simplify.

165.7 Use a calculator.

A. 150.6 in2

B. 131.7 in2

C. 124.6 in2

D. 79 in2

The rectangular matting for a picture frame has a circular cutout as shown in the figure. What is the approximate area of the matting?

Sector – a pie-shaped part of a circle bound by the radius of a circle and an arc

Central angle – an angle whose vertex is the center of a circle and whose sides intersect the circle

Find the Area of a Sector

Find the area of the shaded sector in the circle. Round to the nearest tenth.

Area of a sector

Answer: The area is about 37.7 m2.

Replace N with 120 and r with 6.

Simplify.

Use a calculator.

A. 4.2 in2

B. 16.8 in2

C. 33.5 in2

D. 66.0 in2

To the nearest tenth, what is the area of the shaded sector in the circle?