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

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Example Question #701 : Plane Geometry

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

6

Find the area of the entire figure.

Possible Answers:

Correct answer:

Explanation:

13

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

Example Question #701 : Plane Geometry

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

7

Find the area of the entire figure.

Possible Answers:

Correct answer:

Explanation:

13

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

Example Question #261 : Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

8

Find the area of the entire figure.

Possible Answers:

Correct answer:

Explanation:

13

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

Example Question #701 : Intermediate Geometry

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

9

Find the area of the entire figure.

Possible Answers:

Correct answer:

Explanation:

13

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

Example Question #42 : How To Find The Area Of An Equilateral Triangle

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

10

Find the area of the entire figure.

Possible Answers:

Correct answer:

Explanation:

13

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

Example Question #43 : How To Find The Area Of An Equilateral Triangle

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

11

Find the area of the entire figure.

Possible Answers:

Correct answer:

Explanation:

13

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

Example Question #69 : Equilateral Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

12

Find the area of the entire figure.

Possible Answers:

Correct answer:

Explanation:

13

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

Example Question #70 : Equilateral Triangles

Pyramid

The cube in the above diagram has edges of length 1. Give the area of .

Possible Answers:

Correct answer:

Explanation:

Each of the three triangles , and  has two legs of length 1; therefore, each is an isosceles right triangle, and each is a 45-45-90 triangle. By the 45-45-90 Triangle Theorem, each hypotenuse -  - has length  times that of the legs, or simply . This makes  an equilateral triangle with common sidelength . Using the area formula 

and substituting, the area can be calculated as

.

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