Intermediate Geometry : How to find the area of a sector

Example Questions

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Example Question #21 : Plane Geometry

Find the approximate area of the shaded portion of the figure.

Explanation:

First, you would need to find the diameter of the circle.  Use the Pythagorean Theorem to get

or

Since the diameter is 130, we divide by 2 to get 65 cm for our radius.  Then the area of the circle is

Next we would find the area of each triangle:

and

Then we would subtract these from our answer above to get:

.

Example Question #1 : How To Find The Area Of A Sector

The radius of the circle above is  and .  What is the area of the shaded section of the circle?

Explanation:

Area of Circle = πr2 = π42 = 16π

Total degrees in a circle = 360

Therefore 45 degree slice = 45/360 fraction of circle = 1/8

Shaded Area = 1/8 * Total Area = 1/8 * 16π = 2π

Example Question #31 : Intermediate Geometry

A circle has a diameter of  meters. A certain sector of the circle has a central angle of . Find the area of the sector.

Explanation:

The formula for the area of a sector is.

where  is the radius and  is the measure of the central angle of the sector.

We are given that the diameter of the circle is 60.  Therefore its radius is simply half as long, or 30.

Substituting into our equation gives

Therefore our area is

Example Question #32 : Intermediate Geometry

Find the area of a sector with a central angle of  degrees and a radius of .

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

Solve and round to two decimal places.

Example Question #33 : Intermediate Geometry

Find the area of a sector that has a central angle of  degrees and a radius of .

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

Solve and round to two decimal places.

Example Question #34 : Intermediate Geometry

Find the area of a sector that has a central angle of  degrees and a radius of .

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

Solve and round to two decimal places.

Example Question #35 : Sectors

Find the area of a sector that has a central angle of  degrees and a radius of .

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

Solve and round to two decimal places.

Example Question #36 : Sectors

Find the area of a sector that has a central angle of  degrees and a radius of .

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

Solve and round to two decimal places.

Example Question #31 : Circles

Find the area of a sector that has a central angle of  degrees and a radius of .

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

Solve and round to two decimal places.

Example Question #38 : Sectors

Find the area of a sector that has a central angle of  degrees and a radius of .

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

Solve and round to two decimal places.

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