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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 #872 : Plane Geometry

Find the area of the square.

Possible Answers:

1200

1600

800

900

Correct answer:

800

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.

$\text{Area}=\frac{40^2}{2}$

Solve.

$\text{Area}=800$

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Example Question #35 : How To Find The Perimeter Of A Square

A square has an area of 49in^2 . Find the perimeter.

Possible Answers:

25in

49in

14in

21in

28in

Correct answer:

28in

Explanation:

Since a square has four equal sides, finding the side lengths from the area is quite simple.

Area = Length(Width)

Since all the sides are equal in a square, the length and width are equal, meaning that Area = side ^2 . Plugging in the numbers gives us:

49 = side^2

$\sqrt{}49 = side$

7 = side

Now that we have found the length of each of the sides of the square, we simply add all the sides together, or multiply by 4 (because there are 4 sides in a square).

7(4) = 28in

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Example Question #881 : Plane Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of $2\sqrt2$ .

Possible Answers:

$8\sqrt2$

Correct answer:

Explanation:

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

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{2\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(2)$

Solve.

$\text{Perimeter}=8$

Report an Error

Example Question #37 : How To Find The Perimeter Of A Square

Find the perimeter of a square inscribed in a circle that has a diameter of $3\sqrt2$ .

Possible Answers:

$12\sqrt2$

Correct answer:

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{3\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=3$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(3)$

Solve.

$\text{Perimeter}=12$

Report an Error

Example Question #38 : How To Find The Perimeter Of A Square

Find the perimeter of a square inscribed in a circle that has a diameter of $4\sqrt2$ .

Possible Answers:

$16\sqrt2$

Correct answer:

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{4\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=4$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(4)$

Solve.

$\text{Perimeter}=16$

Report an Error

Example Question #39 : How To Find The Perimeter Of A Square

Find the perimeter of a square inscribed in a circle that has a diameter of $5\sqrt2$ .

Possible Answers:

$20\sqrt2$

$25\sqrt2$

Correct answer:

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{5\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=5$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(5)$

Solve.

$\text{Perimeter}=20$

Report an Error

Example Question #40 : How To Find The Perimeter Of A Square

Find the perimeter of a square inscribed in a circle that has a diameter of $7\sqrt2$ .

Possible Answers:

$28\sqrt2$

Correct answer:

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{7\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=7$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(7)$

Solve.

$\text{Perimeter}=28$

Report an Error

Example Question #881 : Plane Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of $9\sqrt2$ .

Possible Answers:

$36\sqrt2$

$18\sqrt2$

Correct answer:

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{9\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=9$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(9)$

Solve.

$\text{Perimeter}=36$

Report an Error

Example Question #882 : Plane Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of $11\sqrt2$ .

Possible Answers:

$121\sqrt2$

$22\sqrt2$

Correct answer:

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{11\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=11$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(11)$

Solve.

$\text{Perimeter}=44$

Report an Error

Example Question #883 : Plane Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of $13\sqrt2$ .

Possible Answers:

$52\sqrt3$

104

$52\sqrt2$

Correct answer:

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{13\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=13$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(13)$

Solve.

$\text{Perimeter}=52$

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 #872 : Plane Geometry

Example Question #35 : How To Find The Perimeter Of A Square

Example Question #881 : Plane Geometry

Example Question #37 : How To Find The Perimeter Of A Square

Example Question #38 : How To Find The Perimeter Of A Square

Example Question #39 : How To Find The Perimeter Of A Square

Example Question #40 : How To Find The Perimeter Of A Square

Example Question #881 : Plane Geometry

Example Question #882 : Plane Geometry

Example Question #883 : Plane Geometry

All Basic Geometry Resources

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