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Basic Geometry : How to find the area of a square

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #358 : Quadrilaterals

Find the area of a square if it has a diagonal of $2\sqrt7$ .

Possible Answers:

$7\sqrt2$

$7\sqrt3$

$14\sqrt2$

Correct answer:

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

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

Now, use the Pythagorean theorem to find the area of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Substitute in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(2\sqrt7)^2}{2}$

Simplify.

$\text{Area}=\frac{28}{2}$

$\text{Area}=14$

Report an Error

Example Question #359 : Quadrilaterals

Find the area of a square if it has a diagonal of $3\sqrt7$ .

Possible Answers:

$63\sqrt2$

$7\sqrt{10}$

$9\sqrt3$

$\frac{63}{2}$

Correct answer:

$\frac{63}{2}$

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

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

Now, use the Pythagorean theorem to find the area of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Substitute in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(3\sqrt7)^2}{2}$

Simplify.

$\text{Area}=\frac{63}{2}$

Report an Error

Example Question #761 : Plane Geometry

Find the area of a square if it has a diagonal of $\sqrt{26}$ .

Possible Answers:

$13\sqrt3$

$26\sqrt2$

$\frac{13}{2}$

Correct answer:

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

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

Now, use the Pythagorean theorem to find the area of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Substitute in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(\sqrt{26})^2}{2}$

Simplify.

$\text{Area}=\frac{26}{2}$

$\text{Area}=13$

Report an Error

Example Question #762 : Plane Geometry

Find the area of a square if it has a diagonal of $\sqrt{34}$ .

Possible Answers:

$17\sqrt3$

$17\sqrt2$

$\frac{17\sqrt2}{2}$

Correct answer:

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

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

Now, use the Pythagorean theorem to find the area of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Substitute in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(\sqrt{34})^2}{2}$

Simplify.

$\text{Area}=\frac{34}{2}$

$\text{Area}=17$

Report an Error

Example Question #763 : Plane Geometry

Find the area of a square if it has a diagonal of $12\sqrt3$ .

Possible Answers:

$108\sqrt2$

$216\sqrt3$

216

$432\sqrt2$

Correct answer:

216

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

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

Now, use the Pythagorean theorem to find the area of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Substitute in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(12\sqrt3)^2}{2}$

Simplify.

$\text{Area}=\frac{432}{2}$

$\text{Area}=216$

Report an Error

Example Question #363 : Quadrilaterals

Find the area of the square.

Possible Answers:

$84\sqrt2$

882

1764

$1264\sqrt3$

Correct answer:

882

Explanation:

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

Thus, we can use the Pythagorean Theorem to find the length of the sides of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Recall how to find the area of a square.

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Now, substitute in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{42^2}{2}$

Solve.

$\text{Area}=882$

Report an Error

Example Question #364 : Quadrilaterals

Find the area of the square.

Possible Answers:

$968\sqrt2$

1936

968

$224\sqrt3$

Correct answer:

968

Explanation:

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

Thus, we can use the Pythagorean Theorem to find the length of the sides of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Recall how to find the area of a square.

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Now, substitute in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{44^2}{2}$

Solve.

$\text{Area}=968$

Report an Error

Example Question #771 : Plane Geometry

Find the area of the square.

Possible Answers:

$968\sqrt2$

$224\sqrt3$

968

1936

Correct answer:

968

Explanation:

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

Thus, we can use the Pythagorean Theorem to find the length of the sides of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Recall how to find the area of a square.

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Now, substitute in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{44^2}{2}$

Solve.

$\text{Area}=968$

Report an Error

Example Question #772 : Plane Geometry

Find the area of the square.

Possible Answers:

$1152\sqrt2$

$576\sqrt3$

1152

2304

Correct answer:

1152

Explanation:

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

Thus, we can use the Pythagorean Theorem to find the length of the sides of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Recall how to find the area of a square.

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Now, substitute in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{48^2}{2}$

Solve.

$\text{Area}=1152$

Report an Error

Example Question #773 : Plane Geometry

Find the area of the square.

Possible Answers:

1250

$625\sqrt3$

$2500\sqrt2$

$1250\sqrt3$

Correct answer:

1250

Explanation:

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

Thus, we can use the Pythagorean Theorem to find the length of the sides of the square.

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

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

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Recall how to find the area of a square.

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Now, substitute in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{50^2}{2}$

Solve.

$\text{Area}=1250$

Report an Error

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Basic Geometry : How to find the area of a square

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #358 : Quadrilaterals

Example Question #359 : Quadrilaterals

Example Question #761 : Plane Geometry

Example Question #762 : Plane Geometry

Example Question #763 : Plane Geometry

Example Question #363 : Quadrilaterals

Example Question #364 : Quadrilaterals

Example Question #771 : Plane Geometry

Example Question #772 : Plane Geometry

Example Question #773 : Plane Geometry

All Basic Geometry Resources

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