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Basic Geometry : Squares

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 #91 : How To Find The Area Of A Square

Find the area of the square.

Possible Answers:

3136 $\displaystyle 3136$

1998 $\displaystyle 1998$

2428 $\displaystyle 2428$

1568 $\displaystyle 1568$

Correct answer:

1568 $\displaystyle 1568$

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.

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

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

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

Recall how to find the area of a square.

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

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

$\text{Area}=\frac{56^2}{2}$ $\displaystyle \text{Area}=\frac{56^2}{2}$

Solve.

$\text{Area}=1568$ $\displaystyle \text{Area}=1568$

Report an Error

Example Question #121 : Squares

Find the area of the square.

Possible Answers:

1682 $\displaystyle 1682$

2008 $\displaystyle 2008$

3364 $\displaystyle 3364$

4124 $\displaystyle 4124$

Correct answer:

1682 $\displaystyle 1682$

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.

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

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

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

Recall how to find the area of a square.

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

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

$\text{Area}=\frac{58^2}{2}$ $\displaystyle \text{Area}=\frac{58^2}{2}$

Solve.

$\text{Area}=1682$ $\displaystyle \text{Area}=1682$

Report an Error

Example Question #371 : Quadrilaterals

Find the area of the square.

Possible Answers:

2600 $\displaystyle 2600$

3600 $\displaystyle 3600$

2200 $\displaystyle 2200$

1800 $\displaystyle 1800$

Correct answer:

1800 $\displaystyle 1800$

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.

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

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

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

Recall how to find the area of a square.

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

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

$\text{Area}=\frac{60^2}{2}$ $\displaystyle \text{Area}=\frac{60^2}{2}$

Solve.

$\text{Area}=1800$ $\displaystyle \text{Area}=1800$

Report an Error

Example Question #781 : Plane Geometry

Find the area of the square.

Possible Answers:

2888 $\displaystyle 2888$

3844 $\displaystyle 3844$

1922 $\displaystyle 1922$

1666 $\displaystyle 1666$

Correct answer:

1922 $\displaystyle 1922$

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.

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

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

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

Recall how to find the area of a square.

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

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

$\text{Area}=\frac{62^2}{2}$ $\displaystyle \text{Area}=\frac{62^2}{2}$

Solve.

$\text{Area}=1922$ $\displaystyle \text{Area}=1922$

Report an Error

Example Question #93 : How To Find The Area Of A Square

Find the area of a square inscribed in a circle that has a diameter of $\displaystyle 4$.

Possible Answers:

$\displaystyle 16$

$\displaystyle 12$

$\displaystyle 4$

$\displaystyle 8$

Correct answer:

$\displaystyle 8$

Explanation:

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

$\text{Diameter}=\text{Diagonal}$ $\displaystyle \text{Diameter}=\text{Diagonal}$

Thus, we can figure out the diagonal of the square.

$\text{Diagonal}=4$ $\displaystyle \text{Diagonal}=4$

Recall that the diagonal of a square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs. We can then use the Pythagorean Theorem to find the length of the sides of the square.

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

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

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

Now, recall the formula for the area of a square.

$\text{Area of square}=\text{side}^2$ $\displaystyle \text{Area of square}=\text{side}^2$

Thus, we can also write the following formula to find the area of the square:'

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

Plug in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{4^2}{2}=8$ $\displaystyle \text{Area}=\frac{4^2}{2}=8$

Report an Error

Example Question #121 : Squares

Find the area of a square inscribed in a circle that has a diameter of $\displaystyle 24$.

Possible Answers:

576 $\displaystyle 576$

144 $\displaystyle 144$

$\displaystyle 48$

288 $\displaystyle 288$

Correct answer:

288 $\displaystyle 288$

Explanation:

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

$\text{Diameter}=\text{Diagonal}$ $\displaystyle \text{Diameter}=\text{Diagonal}$

Thus, we can figure out the diagonal of the square.

$\text{Diagonal}=4$ $\displaystyle \text{Diagonal}=4$

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

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

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

Now, recall the formula for the area of a square.

$\text{Area of square}=\text{side}^2$ $\displaystyle \text{Area of square}=\text{side}^2$

Thus, we can also write the following formula to find the area of the square:'

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

Plug in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{24^2}{2}=288$ $\displaystyle \text{Area}=\frac{24^2}{2}=288$

Report an Error

Example Question #95 : How To Find The Area Of A Square

Find the area of a square inscribed in a circle that has a diameter of $\displaystyle 25$.

Possible Answers:

$\frac{625}{4}$ $\displaystyle \frac{625}{4}$

$\displaystyle 50$

$\frac{625}{2}$ $\displaystyle \frac{625}{2}$

625 $\displaystyle 625$

Correct answer:

$\frac{625}{2}$ $\displaystyle \frac{625}{2}$

Explanation:

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

$\text{Diameter}=\text{Diagonal}$ $\displaystyle \text{Diameter}=\text{Diagonal}$

Thus, we can figure out the diagonal of the square.

$\text{Diagonal}=4$ $\displaystyle \text{Diagonal}=4$

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

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

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

Now, recall the formula for the area of a square.

$\text{Area of square}=\text{side}^2$ $\displaystyle \text{Area of square}=\text{side}^2$

Thus, we can also write the following formula to find the area of the square:'

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

Plug in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{25^2}{2}=\frac{625}{2}$ $\displaystyle \text{Area}=\frac{25^2}{2}=\frac{625}{2}$

Report an Error

Example Question #122 : Squares

Find the area of a square inscribed in a circle that has a diameter of $\displaystyle 30$.

Possible Answers:

450 $\displaystyle 450$

900 $\displaystyle 900$

$60\sqrt2$ $\displaystyle 60\sqrt2$

$\displaystyle 60$

Correct answer:

450 $\displaystyle 450$

Explanation:

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

$\text{Diameter}=\text{Diagonal}$ $\displaystyle \text{Diameter}=\text{Diagonal}$

Thus, we can figure out the diagonal of the square.

$\text{Diagonal}=4$ $\displaystyle \text{Diagonal}=4$

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

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

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

Now, recall the formula for the area of a square.

$\text{Area of square}=\text{side}^2$ $\displaystyle \text{Area of square}=\text{side}^2$

Thus, we can also write the following formula to find the area of the square:'

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

Plug in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{30^2}{2}=450$ $\displaystyle \text{Area}=\frac{30^2}{2}=450$

Report an Error

Example Question #101 : How To Find The Area Of A Square

Find the area of a square inscribed in a circle that has a diameter of $\displaystyle 32$.

Possible Answers:

512 $\displaystyle 512$

1024 $\displaystyle 1024$

256 $\displaystyle 256$

$32\sqrt2$ $\displaystyle 32\sqrt2$

Correct answer:

512 $\displaystyle 512$

Explanation:

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

$\text{Diameter}=\text{Diagonal}$ $\displaystyle \text{Diameter}=\text{Diagonal}$

Thus, we can figure out the diagonal of the square.

$\text{Diagonal}=4$ $\displaystyle \text{Diagonal}=4$

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

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

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

Now, recall the formula for the area of a square.

$\text{Area of square}=\text{side}^2$ $\displaystyle \text{Area of square}=\text{side}^2$

Thus, we can also write the following formula to find the area of the square:'

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

Plug in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{32^2}{2}=512$ $\displaystyle \text{Area}=\frac{32^2}{2}=512$

Report an Error

Example Question #782 : Basic Geometry

Find the area of a square inscribed in a circle with a diameter of $\displaystyle 34$.

Possible Answers:

1156 $\displaystyle 1156$

$34\sqrt{10}$ $\displaystyle 34\sqrt{10}$

$17\sqrt2$ $\displaystyle 17\sqrt2$

578 $\displaystyle 578$

Correct answer:

578 $\displaystyle 578$

Explanation:

Notice that when a squre is inscribed in a circle, the diameter of the circle is also the diagonal of the square.

$\text{Diameter}=\text{Diagonal}$ $\displaystyle \text{Diameter}=\text{Diagonal}$

Thus, we can figure out the diagonal of the square.

$\text{Diagonal}=4$ $\displaystyle \text{Diagonal}=4$

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

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

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

Now, recall the formula for the area of a square.

$\text{Area of square}=\text{side}^2$ $\displaystyle \text{Area of square}=\text{side}^2$

Thus, we can also write the following formula to find the area of the square:'

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

Plug in the value of the diagonal to find the area of the square.

$\text{Area}=\frac{34^2}{2}=578$ $\displaystyle \text{Area}=\frac{34^2}{2}=578$

Report an Error

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Basic Geometry : Squares

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #91 : How To Find The Area Of A Square

Example Question #121 : Squares

Example Question #371 : Quadrilaterals

Example Question #781 : Plane Geometry

Example Question #93 : How To Find The Area Of A Square

Example Question #121 : Squares

Example Question #95 : How To Find The Area Of A Square

Example Question #122 : Squares

Example Question #101 : How To Find The Area Of A Square

Example Question #782 : Basic Geometry

All Basic Geometry Resources

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