# Basic Geometry : Plane Geometry

## Example Questions

### Example Question #51 : Plane Geometry

Find the area of a circle that has a radius of .

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the area of a circle:

For the circle in question, plug in the given radius to find the area.

### Example Question #52 : Plane Geometry

Find the area of a circle that has a radius of .

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the area of a circle:

For the circle in question, plug in the given radius to find the area.

Remember when multiplying decimals together first move the decimal over so that the number is a whole integer.

Now we multiple the integers together.

From here, we need to move the decimal place back. In this particular problem we moved the decimal over one time for each number for a total of two decimal places.

Therefore our  becomes,

.

### Example Question #53 : Plane Geometry

Find the area of a circle with the radius of .

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the area of a circle:

For the circle in question, plug in the given radius to find the area.

Remember when multiplying decimals together first move the decimal over so that the number is a whole integer.

Now we multiple the integers together.

From here, we need to move the decimal place back. In this particular problem we moved the decimal over one time for each number for a total of two decimal places.

Therefore our  becomes,

.

### Example Question #54 : Plane Geometry

Find the area of a circle whose radius is .

Possible Answers:

Correct answer:

Explanation:

To find area, you must used the following equation.

### Example Question #55 : Plane Geometry

find the area of a circle given the radius is .

Possible Answers:

Correct answer:

Explanation:

To find area, use the following formula:

### Example Question #56 : Plane Geometry

A circle is inscribed in a square that has an area of . What is the area of the circle?

Possible Answers:

The area of the circle cannot be determined.

Correct answer:

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

Plug in the value given for the area to find the side length.

Now, recall how to find the area of a circle.

We also know the relationship between the radius and the diameter.

Use the value you found earlier for the diameter to get the length of the radius.

Plug this value for the radius back into the equation for the area of a circle.

### Example Question #57 : Plane Geometry

A circle is inscribed in a square that has an area of . What is the area of the circle?

Possible Answers:

The area of the circle cannot be determined.

Correct answer:

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

Plug in the value given for the area to find the side length.

Now, recall how to find the area of a circle.

We also know the relationship between the radius and the diameter.

Use the value you found earlier for the diameter to get the length of the radius.

Plug this value for the radius back into the equation for the area of a circle.

### Example Question #58 : Plane Geometry

A circle is inscribed in a square that has an area of . What is the area of the circle?

Possible Answers:

Correct answer:

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

Plug in the value given for the area to find the side length.

Now, recall how to find the area of a circle.

We also know the relationship between the radius and the diameter.

Use the value you found earlier for the diameter to get the length of the radius.

Plug this value for the radius back into the equation for the area of a circle.

### Example Question #51 : Plane Geometry

A circle is inscribed in a square that has an area of . What is the area of the circle?

Possible Answers:

Correct answer:

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

Plug in the value given for the area to find the side length.

Now, recall how to find the area of a circle.

We also know the relationship between the radius and the diameter.

Use the value you found earlier for the diameter to get the length of the radius.

Plug this value for the radius back into the equation for the area of a circle.

### Example Question #51 : Circles

A circle is inscribed in a square that has an area of . What is the area of the circle?

Possible Answers:

Correct answer:

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

Plug in the value given for the area to find the side length.

Now, recall how to find the area of a circle.

We also know the relationship between the radius and the diameter.

Use the value you found earlier for the diameter to get the length of the radius.

Plug this value for the radius back into the equation for the area of a circle.