# Basic Geometry : How to find the area of a circle

## Example Questions

### Example Question #111 : How To Find The Area Of A Circle

If a rectangle with a diagonal of  is inscribed in a circle, what is the area of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall the relationship between the diameter of a circle and its radius:

Substitute in the given diameter to find the radius of the circle.

Simplify.

Finally, recall how to find the area of a circle:

Substitute in the value of the radius to find the area.

Solve.

### Example Question #112 : How To Find The Area Of A Circle

If a rectangle with a diagonal of  is inscribed in a circle, what is the area of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall the relationship between the diameter of a circle and its radius:

Substitute in the given diameter to find the radius of the circle.

Simplify.

Finally, recall how to find the area of a circle:

Substitute in the value of the radius to find the area.

Solve.

### Example Question #113 : How To Find The Area Of A Circle

If a rectangle with a diagonal of  is inscribed in a circle, what is the area of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall the relationship between the diameter of a circle and its radius:

Substitute in the given diameter to find the radius of the circle.

Simplify.

Finally, recall how to find the area of a circle:

Substitute in the value of the radius to find the area.

Solve.

### Example Question #114 : How To Find The Area Of A Circle

If a rectangle with a diagonal of  is inscribed in a circle, what is the area of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall the relationship between the diameter of a circle and its radius:

Substitute in the given diameter to find the radius of the circle.

Simplify.

Finally, recall how to find the area of a circle:

Substitute in the value of the radius to find the area.

Solve.

### Example Question #115 : How To Find The Area Of A Circle

If a rectangle with a diagonal of  is inscribed in a circle, what is the area of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall the relationship between the diameter of a circle and its radius:

Substitute in the given diameter to find the radius of the circle.

Simplify.

Finally, recall how to find the area of a circle:

Substitute in the value of the radius to find the area.

Solve.

### Example Question #116 : How To Find The Area Of A Circle

A rectangle with a diagonal of  is incribed in a circle, what is the area of the circle?

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall the relationship between the diameter of a circle and its radius:

Substitute in the given diameter to find the radius of the circle.

Simplify.

Finally, recall how to find the area of a circle:

Substitute in the value of the radius to find the area.

Solve.

### Example Question #111 : Basic Geometry

Find the area of a circle given radius is .

Explanation:

To solve, simply use the formula for the area of a circle.

Given the radius is , substitute it in for r in the below formula.

Also recall the rules of exponents which states that when an exponent is raised to another exponent, they are multiplied together.

Thus,

### Example Question #118 : How To Find The Area Of A Circle

Find the area of a circle given a radius of 3.

Explanation:

To solve, simply use the formula for the area of a circle.

Thus,

given,

.

### Example Question #119 : How To Find The Area Of A Circle

In the figure below, a circle is inscribed in a square. If the 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 #120 : 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.