Intermediate Geometry : How to find the area of an equilateral triangle

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #21 : How To Find The Area Of An Equilateral Triangle

A circle with a radius of  is inscribed in an equilateral triangle with side lengths of  as shown by the figure below.

1

Find the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

In order to find the area of the shaded region, we must first find the area of the circle and the area of the equilateral triangle.

Recall how to find the area of a circle:

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

Next, recall how to find the area of an equilateral triangle:

Plug in the length of the side of the triangle to find the area.

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the triangle.

Make sure to round to  places after the decimal.

Example Question #22 : How To Find The Area Of An Equilateral Triangle

A circle with a radius of  is inscribed in an equilateral triangle with side lengths of  as shown by the figure below.

1

Find the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

In order to find the area of the shaded region, we must first find the area of the circle and the area of the equilateral triangle.

Recall how to find the area of a circle:

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

Next, recall how to find the area of an equilateral triangle:

Plug in the length of the side of the triangle to find the area.

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the triangle.

Make sure to round to  places after the decimal.

Example Question #23 : How To Find The Area Of An Equilateral Triangle

A circle with a radius of  is inscribed in an equilateral triangle with side lengths of  as shown by the figure below.

1

Find the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

In order to find the area of the shaded region, we must first find the area of the circle and the area of the equilateral triangle.

Recall how to find the area of a circle:

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

Next, recall how to find the area of an equilateral triangle:

Plug in the length of the side of the triangle to find the area.

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the triangle.

Make sure to round to  places after the decimal.

Example Question #24 : How To Find The Area Of An Equilateral Triangle

A circle is placed in an equilateral triangle as shown by the figure.

1

If the radius of the circle is , what is the area of the shaded region?

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, you must first find the areas of the triangle and circle.

First, recall how to find the area of an equilateral triangle:

Substitute in the value of the side to find the area of the triangle.

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

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

Finally, find the area of the shaded region.

Solve and round to two decimal places.

Example Question #25 : How To Find The Area Of An Equilateral Triangle

A circle is placed in an equilateral triangle as shown in the figure.

2

If the radius of the circle is , what is the area of the shaded region?

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, you must first find the areas of the triangle and circle.

First, recall how to find the area of an equilateral triangle:

Substitute in the value of the side to find the area of the triangle.

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

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

Finally, find the area of the shaded region.

Solve and round to two decimal places.

Example Question #26 : How To Find The Area Of An Equilateral Triangle

A circle is placed in an equilateral triangle as shown by the figure.

3

If the radius of the circle is , find the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, you must first find the areas of the triangle and circle.

First, recall how to find the area of an equilateral triangle:

Substitute in the value of the side to find the area of the triangle.

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

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

Finally, find the area of the shaded region.

Solve and round to two decimal places.

Example Question #27 : How To Find The Area Of An Equilateral Triangle

A circle is placed in an equilateral triangle as shown by the figure.

4

If the radius of the circle is , find the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, you must first find the areas of the triangle and circle.

First, recall how to find the area of an equilateral triangle:

Substitute in the value of the side to find the area of the triangle.

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

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

Finally, find the area of the shaded region.

Solve and round to two decimal places.

Example Question #28 : How To Find The Area Of An Equilateral Triangle

A circle is placed in an equilateral triangle as shown in the figure.

5

If the radius of the circle is , find the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, you must first find the areas of the triangle and circle.

First, recall how to find the area of an equilateral triangle:

Substitue in the value of the side to find the area of the triangle.

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

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

Finally, find the area of the shaded region.

Solve and round to two decimal places.

Example Question #29 : How To Find The Area Of An Equilateral Triangle

A circle is placed in an equilateral triangle as shown by the figure.

6

If the radius of the circle is , find the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, you must first find the areas of the triangle and circle.

First, recall how to find the area of an equilateral triangle:

Substitute in the value of the side to find the area of the triangle.

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

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

Finally, find the area of the shaded region.

Solve and round to two decimal places.

Example Question #30 : How To Find The Area Of An Equilateral Triangle

A circle is placed in an equilateral triangle as shown by the figure.

7

If the radius of the circle is , find the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, you must first find the areas of the triangle and circle.

First, recall how to find the area of an equilateral triangle:

Substitute in the value of the side to find the area of the triangle.

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

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

Finally, find the area of the shaded region.

Solve and round to two decimal places.

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