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Basic Geometry : Quadrilaterals

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 #121 : Squares

Find the area of the square.

Possible Answers:

4124

2008

1682

3364

Correct answer:

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.

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

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

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

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.

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

Solve.

$\text{Area}=1682$

Report an Error

Example Question #122 : Squares

Find the area of the square.

Possible Answers:

2600

2200

1800

3600

Correct answer:

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.

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

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

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

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.

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

Solve.

$\text{Area}=1800$

Report an Error

Example Question #781 : Plane Geometry

Find the area of the square.

Possible Answers:

2888

3844

1922

1666

Correct answer:

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.

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

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

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

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.

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

Solve.

$\text{Area}=1922$

Report an Error

Example Question #782 : Plane Geometry

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

Possible Answers:

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.

$\text{Diagonal}=4$

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.

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

Report an Error

Example Question #121 : Squares

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

Possible Answers:

144

288

576

Correct answer:

288

Explanation:

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

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

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.

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

Report an Error

Example Question #784 : Plane Geometry

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

Possible Answers:

$\frac{625}{2}$

$\frac{625}{4}$

625

Correct answer:

$\frac{625}{2}$

Explanation:

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

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

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.

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

Report an Error

Example Question #122 : Squares

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

Possible Answers:

450

900

$60\sqrt2$

Correct answer:

450

Explanation:

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

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

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.

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

Report an Error

Example Question #786 : Basic Geometry

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

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.

$\text{Diagonal}=4$

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

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

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

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.

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

Report an Error

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

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Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #121 : Squares

Example Question #122 : Squares

Example Question #781 : Plane Geometry

Example Question #782 : Plane Geometry

Example Question #121 : Squares

Example Question #784 : Plane Geometry

Example Question #122 : Squares

Example Question #786 : Basic Geometry

Example Question #787 : Basic Geometry

Example Question #788 : Basic Geometry

All Basic Geometry Resources

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