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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #251 : Triangles

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

Find the area of the entire figure.

Possible Answers:

12.12

10.51

8.82

14.21

Correct answer:

12.12

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{2})^2}{4}=\frac{4\sqrt3}{4}=\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(\sqrt3)=12.12$

Make sure to round to places after the decimal.

Report an Error

Example Question #252 : Triangles

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

Find the area of the entire figure.

Possible Answers:

42.19

55.22

The area of the entire figure cannot be determined by the given information.

48.50

Correct answer:

48.50

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{4})^2}{4}=\frac{16\sqrt3}{4}=4\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(4\sqrt3)=48.50$

Make sure to round to places after the decimal.

Report an Error

Example Question #261 : Triangles

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

Find the area of the entire figure.

Possible Answers:

79.77

72.30

75.78

82.30

Correct answer:

75.78

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{5})^2}{4}=\frac{25\sqrt3}{4}$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(\frac{25\sqrt3}{4})=75.78$

Make sure to round to places after the decimal.

Report an Error

Example Question #262 : Triangles

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

Possible Answers:

109.12

112.59

104.97

120.41

Correct answer:

109.12

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(6)^2}{4}=\frac{36\sqrt3}{4}=9\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(9\sqrt3)=109.12$

Make sure to round to places after the decimal.

Report an Error

Example Question #263 : Triangles

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

Find the area of the entire figure.

Possible Answers:

185.23

176.58

198.41

193.99

Correct answer:

193.99

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(8)^2}{4}=\frac{64\sqrt3}{4}=16\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(16\sqrt3)=193.99$

Make sure to round to places after the decimal.

Report an Error

Example Question #703 : Plane Geometry

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

Find the area of the entire figure.

Possible Answers:

501.28

436.48

421.82

491.50

Correct answer:

436.48

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(12)^2}{4}=\frac{144\sqrt3}{4}=36\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(36\sqrt3)=436.48$

Make sure to round to places after the decimal.

Report an Error

Example Question #265 : Triangles

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

Find the area of the entire figure.

Possible Answers:

775.96

741.22

770.29

772.11

Correct answer:

775.96

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(16)^2}{4}=\frac{256\sqrt3}{4}=64\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(64\sqrt3)=775.96$

Make sure to round to places after the decimal.

Report an Error

Example Question #41 : 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.

Find the area of the entire figure.

Possible Answers:

1298.41

1122.01

1145.29

1212.44

Correct answer:

1212.44

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(20)^2}{4}=\frac{400\sqrt3}{4}=100\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(100\sqrt3)=1212.44$

Make sure to round to places after the decimal.

Report an Error

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.

Find the area of the entire figure.

Possible Answers:

1500.67

1682.52

1721.40

1745.91

Correct answer:

1745.91

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(24)^2}{4}=\frac{576\sqrt3}{4}=144\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(144\sqrt3)=1745.91$

Make sure to round to places after the decimal.

Report an Error

Example Question #61 : Equilateral Triangles

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

Find the area of the entire figure.

Possible Answers:

2424.54

2149.20

2205.29

2376.37

Correct answer:

2376.37

Explanation:

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:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

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

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(28)^2}{4}=\frac{784\sqrt3}{4}=196\sqrt3$

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

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(196\sqrt3)=2376.37$

Make sure to round to places after the decimal.

Report an Error

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All Intermediate Geometry Resources

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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #251 : Triangles

Example Question #252 : Triangles

Example Question #261 : Triangles

Example Question #262 : Triangles

Example Question #263 : Triangles

Example Question #703 : Plane Geometry

Example Question #265 : Triangles

Example Question #41 : How To Find The Area Of An Equilateral Triangle

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

Example Question #61 : Equilateral Triangles

All Intermediate Geometry Resources

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