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Basic Geometry : Basic Geometry

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 #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 #781 : Basic Geometry

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

Possible Answers:

576 $\displaystyle 576$

288 $\displaystyle 288$

$\displaystyle 48$

144 $\displaystyle 144$

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 #782 : Basic Geometry

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

Possible Answers:

450 $\displaystyle 450$

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

900 $\displaystyle 900$

$\displaystyle 60$

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 #786 : Basic Geometry

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

Possible Answers:

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

256 $\displaystyle 256$

512 $\displaystyle 512$

1024 $\displaystyle 1024$

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

Example Question #788 : Basic Geometry

Find the area of a square inscribed in a circle that has a diameter of $\displaystyle 36$ .

Possible Answers:

988 $\displaystyle 988$

1296 $\displaystyle 1296$

648 $\displaystyle 648$

338 $\displaystyle 338$

Correct answer:

648 $\displaystyle 648$

Explanation:

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

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

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.

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

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 $\displaystyle 12$ .

Possible Answers:

$24\sqrt2$ $\displaystyle 24\sqrt2$

$6\sqrt2$ $\displaystyle 6\sqrt2$

144 $\displaystyle 144$

$\displaystyle 72$

Correct answer:

$\displaystyle 72$

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.

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

Report an Error

Example Question #381 : Quadrilaterals

Find the area of a square inscribed in a circle that has a diameter of $\displaystyle 14$ .

Possible Answers:

$\displaystyle 63$

$\displaystyle 98$

196 $\displaystyle 196$

$\displaystyle 74$

Correct answer:

$\displaystyle 98$

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.

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

Report an Error

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #781 : Plane Geometry

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

Example Question #781 : Basic Geometry

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

Example Question #782 : Basic Geometry

Example Question #786 : Basic Geometry

Example Question #782 : Basic Geometry

Example Question #788 : Basic Geometry

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

Example Question #381 : Quadrilaterals

All Basic Geometry Resources

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