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 m TU 360 ° Write formula for.

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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 m TU 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 = 936 – [32π + 256] 180 ° = 36(26) – (π 8 2 ) ° ≈ The area is about 579 square feet. Standardized Test Practice The correct answer is C. ANSWER

GUIDED PRACTICE for Examples 3 and 4 4. Find the area of H. SOLUTION Area of sector FHG = Area of H m FG 360 Write formula for area of a sector = Area of H Substitute = Area of H Solve for Area of H. The area of H is cm 2. ANSWER

GUIDED PRACTICE for Examples 3 and 4 5. Find the area of the figure.

GUIDED PRACTICE for Examples 3 and 4 A = b h 1 2 Write formula for area of a triangle. = Substitute. = 24.5 = 24.5 m SOLUTION STEP 1 Take the top as base, which is 7 m and find the area of the triangle

GUIDED PRACTICE for Examples 3 and 4 Area of figure = Area of triangle + Area of semicircle = 19.5 multiply = = m 2 STEP 2 find the area of the semicircle A = π r = π (3.5) 2 2 Write formula for area of a sector. Substitute. STEP 3 Add the areas The area of the figure is about m 2. 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 SOLUTION m A = and if you solve this for m, you get 360 π r 2 360A π r 2