# Intermediate Geometry : How to find the area of a sector

## Example Questions

### Example Question #51 : Intermediate Geometry

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #61 : Sectors

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #62 : Sectors

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #31 : How To Find The Area Of A Sector

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #64 : Sectors

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #65 : Sectors

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #66 : Sectors

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #67 : Sectors

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #68 : Sectors

Find the area of a sector if it has an arc length of  and a radius of .

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

The equation can be simplified to the following:

Plug in the given arc length and radius to find the area of the sector.

Make sure to round to  places after the decimal.

### Example Question #69 : Sectors

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

Explanation:

The circle in question can be drawn as shown by the figure below:

Since the area of a sector is just a fractional part of the area of a circle, we can write the following equation to find the area of a sector:

, where  is the radius of the circle.

Plug in the given central angle and radius to find the area of the sector.

Make sure to round to two places after the decimal.