Ch 11.6 What is the area of a square with an apothem length of 14 in? Round to the nearest tenth if necessary. What is the area of a regular hexagon with.

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Presentation transcript:

Ch 11.6 What is the area of a square with an apothem length of 14 in? Round to the nearest tenth if necessary. 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. Find the area of the figure. Round to the nearest tenth if necessary. A = (14)(4 * 28) = A = (7)(6 * 8) = A rectangle  (8 * 12) = 96 + A triangles  2 (8 * 3) = 24 2 Answer: 120

Ch 11.6 Area of a Circle Standard 8.0 Students know, derive, and solve problems involving the area of common geometric figures. Learning Target: I will be able to solve problems involving areas and sectors of circles. Ch 10.5 Ch 11.6

Vocabulary 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

Concept 1 Ch 11.6 Theorem 11-8

Example 1 Area of a Circle 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 or 88 inches. Divide by 2 to find that the radius is 44 inches. Ch 11.6 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.

Example 1 Area of a Circle Area of a circle Substitution Use a calculator. Ch 11.6 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.

Example 1 A.62.8 ft 2 B ft 2 C ft 2 D ft 2 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. Ch 11.6

Example 2 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. Area of a circle Substitution Divide each side by . Simplify. 4.3 ≈ r Take the positive square root of each side. = r Ch 11.6

Example 2 A.3.8 in. B.4.5 in. C.5.7 in. D.7.6 in. ALGEBRA Find the radius of a circle with an area of 45 square inches. Ch 11.6

Concept 2 Theorem 11-9 Ch 11.6

Example 3 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 1Find 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. Step 2Find 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

Example 3 Area of a Sector Area of a sector x = 36 and r = 4.5 Use a calculator. Ch 11.6 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?

Example 3 A in 2 B in 2 C in 2 D in 2 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? Ch 11.6