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Advanced Geometry : Solid Geometry

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

Example Question #5 : How To Find The Surface Area Of A Tetrahedron

In terms of , find the surface area of a regular tetrahedron with side lengths of .

Possible Answers:

$27q^2\sqrt3$

$3q\sqrt3$

$9q^2\sqrt3$

$9q\sqrt3$

Correct answer:

$9q^2\sqrt3$

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation.

$\text{Surface Area}=\sqrt3(3q)^2=9q^2\sqrt3$

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Example Question #1 : How To Find The Surface Area Of A Tetrahedron

The surface area of a regular tetrahedron is $36\sqrt3$ . If the length of each side is , find the value of .

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation.

$36\sqrt3=\sqrt3(3a)^2$

Now, solve for .

9a^2=36

a^2=4

a=2

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Example Question #2 : How To Find The Surface Area Of A Tetrahedron

The surface area of a regular tetrahedron is . If each side length is , find the value of . Round to the nearest tenths place.

Possible Answers:

8.4

1.7

2.4

0.9

Correct answer:

0.9

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation.

$54=\sqrt3(6x)^2$

Solve for .

$36x^2\sqrt3=54$

$x^2\sqrt3=1.5$

$x^2=\frac{1.5}{\sqrt3}=0.866$

$x=\sqrt{0.866}=0.9$

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Example Question #5 : How To Find The Surface Area Of A Tetrahedron

The surface area of a regular tetrahedron is . If each side length is , find the value of . Round to the nearest tenths place.

Possible Answers:

0.7

1.5

2.3

1.9

Correct answer:

1.5

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation.

$64=\sqrt3(4x)^2$

$16x^2=\frac{64}{\sqrt3}$

$x^2=\frac{64}{16\sqrt3}=2.309$

x=1.5

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Example Question #6 : How To Find The Surface Area Of A Tetrahedron

The surface area of a regular tetrahedron is $100\sqrt3$ . If each side length is x-1 , find the value of .

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation and solve for .

$100\sqrt3=\sqrt3(x-1)^2$

(x-1)^2=100

x^2-2x+1=100

x^2-2x-99=0

(x-11)(x+9)=0

x=11, x=-9

Since we are dealing with a 3-dimensional shape, only x=11 is valid.

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Example Question #61 : Solid Geometry

In terms of , find the surface area of a regular tetrahedron with side lengths .

Possible Answers:

$81c^2\sqrt3$

$281c^2\sqrt3$

$9c^2\sqrt3$

$81c\sqrt3$

Correct answer:

$81c^2\sqrt3$

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation.

$\text{Surface Area}=\sqrt3(9c)^2=81c^2\sqrt3$

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Example Question #62 : Solid Geometry

Find the surface area of a regular tetrahedron with a side length of $\frac{1}{2}$ .

Possible Answers:

$\frac{\sqrt3}{8}$

$\frac{\sqrt3}{6}$

$\frac{\sqrt3}{2}$

$\frac{\sqrt3}{4}$

Correct answer:

$\frac{\sqrt3}{4}$

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation.

$\text{Surface Area}=\sqrt3\left(\frac{1}{2}\right)^2=\frac{\sqrt3}{4}$

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Example Question #63 : Solid Geometry

In terms of , find the surface area of a regular tetrahedron with a side length of $\frac{1}{4}z$ .

Possible Answers:

$16z^2\sqrt3$

$\frac{\sqrt3}{16z^2}$

$\frac{16\sqrt3}{z^2}$

$\frac{z^2\sqrt3}{16}$

Correct answer:

$\frac{z^2\sqrt3}{16}$

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation.

$\text{Surface Area}=\sqrt3\left(\frac{z}{4}\right)^2=\frac{z^2\sqrt3}{16}$

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Example Question #64 : Solid Geometry

The surface area of a regular tetrahedron is $16\sqrt3$ . If each side length is , find the value of .

Possible Answers:

$4\sqrt2$

Correct answer:

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

$\text{Surface Area}=\sqrt3 (side^2)$

Now, substitute in the value of the side length into the equation.

$16\sqrt3=\sqrt3(2x)^2$

Now, solve for .

16=4x^2

x^2=4

$x=\sqrt4=2$

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Example Question #71 : Solid Geometry

If the edge length of a tetrahedron is $\sqrt3$ , what is the surface area of the tetrahedron?

Possible Answers:

$3\sqrt3$

$9\sqrt3$

$\sqrt6$

Correct answer:

$3\sqrt3$

Explanation:

Write the formula for finding the surface area of a tetrahedron.

$A=\sqrt3 s^2$

Substitute the edge and solve.

$A=\sqrt3 (\sqrt3)^2 = \sqrt3 (3) = 3\sqrt3$

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Advanced Geometry : Solid Geometry

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #5 : How To Find The Surface Area Of A Tetrahedron

Example Question #1 : How To Find The Surface Area Of A Tetrahedron

Example Question #2 : How To Find The Surface Area Of A Tetrahedron

Example Question #5 : How To Find The Surface Area Of A Tetrahedron

Example Question #6 : How To Find The Surface Area Of A Tetrahedron

Example Question #61 : Solid Geometry

Example Question #62 : Solid Geometry

Example Question #63 : Solid Geometry

Example Question #64 : Solid Geometry

Example Question #71 : Solid Geometry

All Advanced Geometry Resources

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