Question

What is the area of a sector with a central angle of 185 and a diameter of 6.4

Answer 1

Geometry B Unit 5: Area - Lesson 10: Area Unit Test

1. What is the area of the trapezoid? The diagram is not drawn to scale.

72 cm^2

2. Given the regular polygon, what is the measure of each numbered angle?

m∡1 = 36°; m∡2 = 72°

3. What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.

5/2 and 25/4

4. What is the area of a regular pentagon with a side of 12 in.? Round the answer to the nearest tenth.

247.7 in.2

5. Name the minor arc and find its measure.

AB; 162°

6. What is the circumference of the given circle in terms of pi_symbol?

28pi in.

7. What is the area of the given circle in terms of pi?

10.89pi m^2

8. What is the area of a sector with a central angle of 185° and a diameter of 6.4 m? Round the answer to the nearest tenth.

16.5 m^2

9. What is the area of the shaded region in the given circle in terms of pi_symbol and in simplest form?

(270 pi + 81 Root 3) m^2

Answer 2

The area is 16.52.

The central angle is 185; this means that the sector makes up 185/360 of the total circle.

We will multiply this fraction by the area of the total circle. The area of a circle is given by A = πr². Since the diameter is 6.4, the radius is 6.4/2 = 3.2:

A = 3.14(3.2)² = 32.1536

We multiply this by the fraction of the circle the sector represents:
185/360(32.1536) = 16.52