Basic Geometry : How to find the area of a circle

Example Questions

Example Question #121 : Basic Geometry

In the figure below, a circle is inscribed in a square. If the length of a side of the square is , what is the area of the shaded region?

The area of the shaded region cannot be determined.

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #121 : Circles

In the figure below, a circle is inscribed in a square. If a side length of the square is , what is the area of the shaded region?

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #123 : Basic Geometry

In the figure below, a circle is inscribed in a square. If a length of the side of the square is , what is the area of the shaded region?

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #124 : Basic Geometry

In the figure below, a circle is inscribed in a square. If a length of the side of the square is , what is the area of the shaded region?

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #121 : Basic Geometry

In the figure below, a circle is inscribed in a square. If the length of a side of the square is , what is the area of the shaded region?

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #121 : How To Find The Area Of A Circle

In the figure below, a circle is inscribed in a square. If the length of a side of the square is , what is the area of the shaded region?

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #127 : Basic Geometry

In the figure below, a circle is inscribed in a square. If the length of a side of the square is , what is the area of the shaded region?

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #122 : How To Find The Area Of A Circle

In the figure below, a circle is inscribed in a square. If the length of a side of the square is , what is the area of the shaded region?

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #129 : Basic Geometry

In the figure below, a circle is inscribed in a square. If the length of a side of the square is , find the area of the shaded region.

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.

Example Question #130 : Basic Geometry

In the figure below, a circle is inscribed in a square. If the length of a side of the square is , what is the area of the shaded region?

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

Plug in the given value to find the area of the square.

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

Plug in the value of the diameter to find the length of the radius.

Now, recall the formula to find the area of a circle:

Plug in the value of the radius to find the area of the circle.

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

Round to two places after the decimal.