Find the area of a circle with the given measure. 2. Radius: 1 3 mi 1. Radius: 8 cm ANSWER about 201.06 cm2 ANSWER about 5.59 mi2 4. Solve x2 = 100 π . 3. Circumference: 4π ft ANSWER 4π ft2 ANSWER about _ + 5.64

Vocabulary   Sector of a circle – the region bounded by two radii of the circle and their intercepted arc Area of a Sector Theorem 11.2 – area of sector : area of circle = arc measure : 360

Use the formula for area of a circle EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. SOLUTION a. Area r = 2.5 cm A = πr2 Write formula for the area of a circle. = π (2.5)2 Substitute 2.5 for r. = 6.25π Simplify. ≈ 19.63 Use a calculator. The area of A is about 19.63 square centimeters. ANSWER

Use the formula for area of a circle EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. SOLUTION A = 113.1 cm2 b. Diameter A = πr2 Write formula for the area of a circle. 113.1 = πr2 Substitute 113.1 for A. = r2 113.1 π Divide each side by π. 6 ≈ r Find the positive square root of each side. The radius is about 6 cm, so the diameter is about 12 centimeters. ANSWER

Find the areas of the sectors formed by UTV. EXAMPLE 2 Find areas of sectors Find the areas of the sectors formed by UTV. SOLUTION STEP 1 Find the measures of the minor and major arcs. Because m UTV = 70° , mUV = 70° and mUSV = 360° – 70° = 290°. STEP 2 Find the areas of the small and large sectors. Area of small sector = πr2 mUV 360° Write formula for area of a sector. = π 82 70° 360° Substitute. ≈ 39.10 Use a calculator.

Area of large sector = πr2 mUSV 360° EXAMPLE 2 Find areas of sectors Area of large sector = πr2 mUSV 360° Write formula for area of a sector. = π 82 290° 360° Substitute. ≈ 161.97 Use a calculator. The areas of the small and large sectors are about 39.10 square units and 161.97 square units, respectively. ANSWER

GUIDED PRACTICE for Examples 1 and 2 Use the diagram to find the indicated measure. about 615.75 ft2 ANSWERS 1. Area of D Area of red sector about 205.25 ft2 Area of blue sector about 410.50 ft2

Use the Area of a Sector Theorem EXAMPLE 3 Use the Area of a Sector Theorem Use the diagram to find the area of V. SOLUTION Area of sector TVU = Area of V mTU 360° Write formula for area of a sector. 35 = Area of V 40° 360° Substitute. 315 = Area of V Solve for Area of V. The area of V is 315 square meters. ANSWER

EXAMPLE 4 Standardized Test Practice SOLUTION The area you need to paint is the area of the rectangle minus the area of the entrance. The entrance can be divided into a semicircle and a square.

EXAMPLE 4 Standardized Test Practice 180° = 36(26) – (π 82 ) + 162 360° = 936 – [32π + 256] ≈ 579.47 The area is about 579 square feet. The correct answer is C. ANSWER

GUIDED PRACTICE for Examples 3 and 4 4. Find the area of H. 5. Find the area of the figure. about 907.92 cm2 ANSWER about 43.74 m2 ANSWER

GUIDED PRACTICE for Examples 3 and 4 6. If you know the area and radius of a sector of a circle, can you find the measure of the intercepted arc? Explain. Yes; the formula for the area of sector is m A = and if you solve this for m, you get m = 360 π r2 360A . ANSWER

Daily Homework Quiz Find the area of the sectors formed by DEF. Use the area of the sector to find the area of R ANSWER 106.03 in.2, 141.31 in.2 ANSWER 211.09 cm2

Daily Homework Quiz 3. Find the area of the shaded region. ANSWER 23.18 ft2