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Basic Geometry : Quadrilaterals

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Example Questions

Example Question #711 : Plane Geometry

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

Possible Answers:

256

169

289

321

Correct answer:

256

Explanation:

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

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

From this equation, we can solve for the side length of a square.

$\text{Side length}=\frac{\text{Perimeter}}{4}$

For the given square,

$\text{Side length}=\frac{64}{4}=16$

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

$\text{Area}=\text{side length}^2$

For the square in question, we can plug in the side length we found from the perimeter to find the area.

$\text{Area}=16^2=256$

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Example Question #712 : Plane Geometry

If the perimeter of the square is 328 , what is the area of the square?

Possible Answers:

8744

6239

6724

5974

Correct answer:

6724

Explanation:

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

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

From this equation, we can solve for the side length of a square.

$\text{Side length}=\frac{\text{Perimeter}}{4}$

For the given square,

$\text{Side length}=\frac{328}{4}=82$

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

$\text{Area}=\text{side length}^2$

For the square in question, we can plug in the side length we found from the perimeter to find the area.

$\text{Area}=82^2=6724$

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Example Question #311 : Quadrilaterals

If the perimeter of a square is 220 , what is the area of the square?

Possible Answers:

2225

4065

3025

5025

Correct answer:

3025

Explanation:

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

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

From this equation, we can solve for the side length of a square.

$\text{Side length}=\frac{\text{Perimeter}}{4}$

For the given square,

$\text{Side length}=\frac{220}{4}=55$

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

$\text{Area}=\text{side length}^2$

For the square in question, we can plug in the side length we found from the perimeter to find the area.

$\text{Area}=55^2=3025$

Report an Error

Example Question #312 : Quadrilaterals

If the diagonal of a square is $6\sqrt2$ , what is the area of the square?

Possible Answers:

Correct answer:

Explanation:

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

We can then use the Pythgorean Theorem to write the following equations:

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

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

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

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

Now, use this formula and substitute using the given values to find the side length of the square.

$\text{Side length}=\frac{6\sqrt2}{\sqrt2}$

Simplify.

$\text{Side length}=6$

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

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

For this square in question,

$\text{Area}=6^2$

Solve.

$\text{Area}=36$

Report an Error

Example Question #313 : Quadrilaterals

If the diagonal of a square is $5\sqrt2$ , what is the area of the square?

Possible Answers:

Correct answer:

Explanation:

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

We can then use the Pythgorean Theorem to write the following equations:

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

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

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

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

Now, use this formula and substitute using the given values to find the side length of the square.

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

Simplify.

$\text{Side length}=5$

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

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

For this square in question,

$\text{Area}= 5 ^ 2$

Solve.

$\text{Area}= 25$

Report an Error

Example Question #37 : How To Find The Area Of A Square

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

Possible Answers:

200

100

150

Correct answer:

100

Explanation:

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

We can then use the Pythgorean Theorem to write the following equations:

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

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

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

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

Now, use this formula and substitute using the given values to find the side length of the square.

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

Simplify.

$\text{Side length}=10$

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

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

For this square in question,

$\text{Area}= 10 ^2$

Solve.

$\text{Area}= 100$

Report an Error

Example Question #314 : Quadrilaterals

If the diagonal of a square is $8\sqrt2$ , what is the area of the square?

Possible Answers:

Correct answer:

Explanation:

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

We can then use the Pythgorean Theorem to write the following equations:

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

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

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

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

Now, use this formula and substitute using the given values to find the side length of the square.

$\text{Side length}=\frac{8\sqrt2}{\sqrt2}$

Simplify.

$\text{Side length}=8$

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

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

For this square in question,

$\text{Area}= 8 ^2$

Solve.

$\text{Area}=64$

Report an Error

Example Question #315 : Quadrilaterals

If the diagonal of a square is $12\sqrt2$ , what is the area of the square?

Possible Answers:

121

144

Correct answer:

144

Explanation:

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

We can then use the Pythgorean Theorem to write the following equations:

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

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

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

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

Now, use this formula and substitute using the given values to find the side length of the square.

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

Simplify.

$\text{Side length}=12$

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

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

For this square in question,

$\text{Area}= 12 ^2$

Solve.

$\text{Area}= 144$

Report an Error

Example Question #316 : Quadrilaterals

If the diagonal of a square is $13\sqrt2$ , what is the area of the square?

Possible Answers:

169

Correct answer:

169

Explanation:

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

We can then use the Pythgorean Theorem to write the following equations:

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

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

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

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

Now, use this formula and substitute using the given values to find the side length of the square.

$\text{Side length}=\frac{13\sqrt2}{\sqrt2}$

Simplify.

$\text{Side length}=13$

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

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

For this square in question,

$\text{Area}= 13 ^2$

Solve.

$\text{Area}= 169$

Report an Error

Example Question #43 : How To Find The Area Of A Square

If the diagonal of a square is $\frac{\sqrt2}{2}$ , what is the area of the square?

Possible Answers:

$\frac{\sqrt2}{4}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{2\sqrt2}{3}$

Correct answer:

$\frac{1}{4}$

Explanation:

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

We can then use the Pythgorean Theorem to write the following equations:

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

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

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

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

Now, use this formula and substitute using the given values to find the side length of the square.

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

Dividing a fraction by a number is the same as multiplying by its reciprocal.

$\text{Side length}=\frac{\sqrt2}{2}\times\frac{1}{\sqrt2}$

Simplify.

$\text{Side length}=\frac{1}{2}$

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

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

For this square in question,

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

Solve.

$\text{Area}= \frac{1}{4}$

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 #711 : Plane Geometry

Example Question #712 : Plane Geometry

Example Question #311 : Quadrilaterals

Example Question #312 : Quadrilaterals

Example Question #313 : Quadrilaterals

Example Question #37 : How To Find The Area Of A Square

Example Question #314 : Quadrilaterals

Example Question #315 : Quadrilaterals

Example Question #316 : Quadrilaterals

Example Question #43 : How To Find The Area Of A Square

All Basic Geometry Resources

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