Ch 11.6

What is the area of a regular hexagon with side length of 8 cm and apothem of 7 cm? Round to the nearest tenth if necessary.

A = (7)(6 * 8) = 168 2 What is the area of a square with an apothem length of 14 in? Round to the nearest tenth if necessary.

A = (14)(4 * 28) = 784 2 Find the area of the figure. Round to the nearest tenth if necessary.

A rectangle + A triangles

 

(8 * 12) = 96 2 (8 * 3) = 24 2 Answer: 120

Ch 11.6

Area of a Circle

Learning Target: I will be able to solve problems involving areas and sectors of circles.

Standard 8.0

Students know, derive, and solve problems involving the area of common geometric figures.

Ch 11.6

radius

a segment of a circle whose endpoints are the center of the circle and a point on the circle.

sector

a region of a circle bounded by a central angle and its corresponding arc.

Ch 11.6

Theorem 11-8

Ch 11.6

Area of a Circle MANUFACTURING An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches.

The diameter of the umbrella is 72 inches, and the cover must extend 8 inches in each direction. So, the diameter of the cover is 8 + 72 + 8 or 88 inches. Divide by 2 to find that the radius is 44 inches.

Ch 11.6

Area of a Circle MANUFACTURING An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches.

Area of a circle Substitution Use a calculator.

Ch 11.6

A swimming pool company manufactures circular covers for above ground pools. If the cover is 1 foot longer than the pool on each side, find the area of the cover.

A.

B.

C.

D.

62.8 ft 2 254.5 ft 2 314.2 ft 2 1256.6 ft 2

Ch 11.6

Use the Area of a Circle to Find a Missing Measure ALGEBRA Find the radius of a circle with an area of 58 square inches.

=

r

4.3 ≈

r

Area of a circle Substitution Divide each side by  .

Take the positive square root of each side.

Simplify.

Ch 11.6

ALGEBRA Find the radius of a circle with an area of 45 square inches.

A.

3.8 in.

B.

4.5 in.

C.

5.7 in.

D.

7.6 in.

Ch 11.6

Theorem 11-9

Ch 11.6

Area of a Sector PIE A pie has a diameter of 9 inches and is cut into 10 congruent slices. What is the area of one slice to the nearest hundredth? Step 1 Step 2

Find the arc measure of a pie slice.

Since the pie is equally divided into 10 slices, each slice will have an arc measure of 360 ÷ 10 or 36.

Find the radius of the pie. Use this measure to find the area of the sector, or slice.

The diameter is 9 inches, so the radius is 4.5 inches.

Ch 11.6

Area of a Sector PIE A pie has a diameter of 9 inches and is cut into 10 congruent slices. What is the area of one slice to the nearest hundredth?

Area of a sector

x

= 36 and

r

= 4.5

Use a calculator.

Ch 11.6

PIZZA A pizza has a diameter of 14 inches and is cut into 8 congruent slices. What is the area of one slice to the nearest hundredth? A.

16.21 in 2 B.

19.24 in 2 C.

26.43 in 2 D.

38.48 in 2