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Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #869 : Plane Geometry

If the diagonal of a square is $14\sqrt2$ , what is the perimeter of the square?

Possible Answers:

196

Correct answer:

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{14\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=14$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 14$

Solve.

$\text{Perimeter}=56$

Report an Error

Example Question #870 : Plane Geometry

If the diagonal of a square is $10\sqrt2$ , what is the perimeter of the square?

Possible Answers:

Correct answer:

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{10\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=10$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 10$

Solve.

$\text{Perimeter}=40$

Report an Error

Example Question #463 : Quadrilaterals

If the diagonal of a square is $9\sqrt2$ , what is the perimeter of the square?

Possible Answers:

Correct answer:

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{9\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=9$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 9$

Solve.

$\text{Perimeter}=36$

Report an Error

Example Question #464 : Quadrilaterals

If the diagonal of a square is $22\sqrt2$ , what is the perimeter of the square?

Possible Answers:

484

176

Correct answer:

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{22\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=22$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 22$

Solve.

$\text{Perimeter}=88$

Report an Error

Example Question #465 : Quadrilaterals

If the diagonal of a square is $23\sqrt2$ , what is the perimeter of the square?

Possible Answers:

102

Correct answer:

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{23\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=23$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 23$

Solve.

$\text{Perimeter}= 92$

Report an Error

Example Question #461 : Quadrilaterals

If the diagonal of a square is $56\sqrt2$ , what is the perimeter of the square?

Possible Answers:

236

112

324

224

Correct answer:

224

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{56\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=56$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 56$

Solve.

$\text{Perimeter}=224$

Report an Error

Example Question #467 : Quadrilaterals

If the diagonal of a square is $236\sqrt2$ , what is the perimeter of the square?

Possible Answers:

784

944

1024

487

Correct answer:

944

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{236\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=236$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 236$

Solve.

$\text{Perimeter}=944$

Report an Error

Example Question #31 : How To Find The Perimeter Of A Square

If the diagonal of a square is , what is the perimeter of the square?

Possible Answers:

$15\sqrt2$

$10\sqrt2$

$20\sqrt2$

Correct answer:

$20\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{10}{\sqrt{2}}=\frac{10\sqrt2}{2}=5\sqrt2$

Multiply the top and bottom of the fraction by one in the form of $\frac{\sqrt{2}}{\sqrt{2}}$

$\text{Side length}=\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{Side length}=\frac{10\sqrt2}{2}$

Simplify.

$\text{Side length}=5\sqrt2$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 5\sqrt2$

Solve.

$\text{Perimeter}=20\sqrt2$

Report an Error

Example Question #32 : How To Find The Perimeter Of A Square

If the diagonal of a square is , what is the perimeter of the square?

Possible Answers:

$24\sqrt2$

$48\sqrt2$

Correct answer:

$48\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of one side of the square.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{24}{\sqrt{2}}$

Multiply the top and bottom of the fraction by one in the form of $\frac{\sqrt{2}}{\sqrt{2}}$

$\text{Side length}=\frac{24}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{Side length}=\frac{24\sqrt2}{2}$

Simplify.

$\text{Side length}=12\sqrt2$

Now, recall how to find the perimeter of a square.

$\text{Perimeter}=4\times\text{side length}$

For the square in question,

$\text{Perimeter}=4\times 12\sqrt2$

Solve.

$\text{Perimeter}=48\sqrt2$

Report an Error

Example Question #461 : Quadrilaterals

Find the perimeter of a square given area is .

Possible Answers:

Correct answer:

Explanation:

To find perimeter, we must first find the side length and then multiply is by .

$A=s^2\Rightarrow s=\sqrt{A}=\sqrt{49}=7$

$P=4s=4\cdot7=28$

Report an Error

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Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #869 : Plane Geometry

Example Question #870 : Plane Geometry

Example Question #463 : Quadrilaterals

Example Question #464 : Quadrilaterals

Example Question #465 : Quadrilaterals

Example Question #461 : Quadrilaterals

Example Question #467 : Quadrilaterals

Example Question #31 : How To Find The Perimeter Of A Square

Example Question #32 : How To Find The Perimeter Of A Square

Example Question #461 : Quadrilaterals

All Basic Geometry Resources

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