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 VmTU360°

Write formula for area of a sector.

35 = Area of V40°

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 82 ) + 162

360°

≈ 579.47

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 HmFG360 Write formula

for area of a sector.

214.37 = Area of H85360

Substitute.

907.92 = Area of H Solve for Area of H.

The area of H is 907.92 cm2.

ANSWER

GUIDED PRACTICE for Examples 3 and 4

5. Find the area of the figure.

GUIDED PRACTICE for Examples 3 and 4

A = b h12 Write formula for area of a

triangle.

= 7 712 Substitute.

= 24.5

= 24.5 m

SOLUTION

STEP 1Take 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

= 24.5 + 19.5

= 43.74 m2

STEP 2 find the area of the semicircle

A = π r2121= 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 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

SOLUTION

mA = and if you solve this for m, you get

360π r2

360Aπ r2