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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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Example Questions

Example Question #786 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

$32\sqrt2$

256

512

1024

Correct answer:

512

Explanation:

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

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

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

$\text{Diagonal}=4$

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.

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

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

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

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

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

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

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

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

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

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Example Question #787 : Basic Geometry

Find the area of a square inscribed in a circle with a diameter of .

Possible Answers:

$17\sqrt2$

578

$34\sqrt{10}$

1156

Correct answer:

578

Explanation:

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

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

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

$\text{Diagonal}=4$

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

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

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

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

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

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

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

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

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

Report an Error

Example Question #788 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

988

1296

648

338

Correct answer:

648

Explanation:

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

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

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

$\text{Diagonal}=4$

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

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

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

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

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

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

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

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

$\text{Area}=\frac{36^2}{2}=648$

Report an Error

Example Question #783 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

144

$6\sqrt2$

$24\sqrt2$

Correct answer:

Explanation:

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

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

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

$\text{Diagonal}=4$

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

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

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

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

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

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

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

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

$\text{Area}=\frac{12^2}{2}=72$

Report an Error

Example Question #790 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

196

Correct answer:

Explanation:

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

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

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

$\text{Diagonal}=4$

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

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

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

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

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

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

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

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

$\text{Area}=\frac{14^2}{2}=98$

Report an Error

Example Question #104 : How To Find The Area Of A Square

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

128

112

256

362

Correct answer:

128

Explanation:

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

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

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

$\text{Diagonal}=4$

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

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

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

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

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

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

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

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

$\text{Area}=\frac{16^2}{2}=128$

Report an Error

Example Question #105 : How To Find The Area Of A Square

Find the area of a square inscribed in a circle that has a diameter of .

Possible Answers:

162

810

324

486

Correct answer:

162

Explanation:

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

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

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

$\text{Diagonal}=4$

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

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

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

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

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

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

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

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

$\text{Area}=\frac{18^2}{2}=162$

Report an Error

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

Find the area of a square inscribed in a circle with a diameter of 100 .

Possible Answers:

5000

10000

1000

500

Correct answer:

5000

Explanation:

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

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

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

$\text{Diagonal}=4$

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

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

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

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

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

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

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

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

$\text{Area}=\frac{100^2}{2}=5000$

Report an Error

Example Question #791 : Basic Geometry

Find the area of a square given side length 3x^2 .

Possible Answers:

9x^4

3x^4

9x^2

6x^4

Correct answer:

9x^4

Explanation:

To solve, simply use the formula for the area of a square and remember to distribute the square to both the constant and the variable. Thus,

A=s^2=(3x^2)^2=3^2*(x^2)^2=9x^4

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Example Question #792 : Basic Geometry

Find the area of a square given side length of 4.

Possible Answers:

Correct answer:

Explanation:

To find the area of a square multiply the width with the length. In the case of a square, all sides are the same length thus, the area is simply the side length squarred.

To solve, simply use the formula for the area of a square and let,

s=4 .

Thus,

A=s^2=4^2=16 .

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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 #786 : Basic Geometry

Example Question #787 : Basic Geometry

Example Question #788 : Basic Geometry

Example Question #783 : Basic Geometry

Example Question #790 : Basic Geometry

Example Question #104 : How To Find The Area Of A Square

Example Question #105 : How To Find The Area Of A Square

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

Example Question #791 : Basic Geometry

Example Question #792 : Basic Geometry

All Basic Geometry Resources

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