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Basic Geometry : Plane 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 #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 #222 : Squares

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

Possible Answers:

$18\sqrt2$

$36\sqrt2$

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

Example Question #231 : Squares

Find the perimeter of a square inscribed in a circle that has a diameter of $15\sqrt2$ .

Possible Answers:

180

120

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.

$\text{side}=\frac{15\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=15$

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.

$\text{Perimeter}=4(15)$

Solve.

$\text{Perimeter}=60$

Report an Error

Example Question #881 : Basic Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of $12\sqrt2$ .

Possible Answers:

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.

$\text{side}=\frac{12\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=12$

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.

$\text{Perimeter}=4(12)$

Solve.

$\text{Perimeter}=48$

Report an Error

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

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 #222 : Squares

Example Question #882 : Plane Geometry

Example Question #883 : Plane Geometry

Example Question #231 : Squares

Example Question #881 : Basic Geometry

All Basic Geometry Resources

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