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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 #491 : Quadrilaterals

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

Possible Answers:

200

160

$80\sqrt2$

$40\sqrt2$

Correct answer:

$80\sqrt2$

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.

$\text{side}=\frac{40(\sqrt2)}{2}$

Simplify.

$\text{side}=20\sqrt2$

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.

$\text{Perimeter}=4(20\sqrt2)$

Solve.

$\text{Perimeter}=80\sqrt2$

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Example Question #492 : Quadrilaterals

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

Possible Answers:

176

$44\sqrt2$

$88\sqrt2$

$132\sqrt2$

Correct answer:

$88\sqrt2$

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.

$\text{side}=\frac{44(\sqrt2)}{2}$

Simplify.

$\text{side}=22\sqrt2$

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.

$\text{Perimeter}=4(22\sqrt2)$

Solve.

$\text{Perimeter}=88\sqrt2$

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Example Question #493 : Quadrilaterals

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

Possible Answers:

$120\sqrt2$

$180\sqrt2$

$60\sqrt2$

240

Correct answer:

$120\sqrt2$

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.

$\text{side}=\frac{60(\sqrt2)}{2}$

Simplify.

$\text{side}=30\sqrt2$

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.

$\text{Perimeter}=4(30\sqrt2)$

Solve.

$\text{Perimeter}=120\sqrt2$

Report an Error

Example Question #494 : Quadrilaterals

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

Possible Answers:

$152\sqrt2$

$144\sqrt2$

304

$76\sqrt2$

Correct answer:

$152\sqrt2$

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.

$\text{side}=\frac{76(\sqrt2)}{2}$

Simplify.

$\text{side}=38\sqrt2$

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.

$\text{Perimeter}=4(38\sqrt2)$

Solve.

$\text{Perimeter}=152\sqrt2$

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Example Question #901 : Plane Geometry

Find the perimeter of a square whose side length is 7.

Possible Answers:

Correct answer:

Explanation:

The perimeter of a square is found by adding all the side lengths together. In a square there are two widths, two lengths, and they are equal.

In other words, simply use the formula for the perimeter of a square and let,

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

s=7

thus,

P=4s=4*7=28 .

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Example Question #61 : How To Find The Perimeter Of A Square

Find the perimeter of a square with side length 2.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a square. Thus,

A=4s=4*2=8

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Example Question #62 : How To Find The Perimeter Of A Square

Find the perimeter of a square with side length of 2.

Possible Answers:

$2\sqrt2$

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a square. Thus,

P=4s=4*2=8

If the formula escapes you, simply sum the sides. However, you must know that all the sides in a square are equal in order to add them up. Since they are equal, the formula just shows you that you can multiply one side by 4 instead of adding them all together.

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Example Question #61 : How To Find The Perimeter Of A Square

A square garden was made to put 8 plants that are 1.25 feet wide each on each side. The corner plants were included in two sides. What is the length of the perimeter?

Possible Answers:

50ft

10ft

20ft

30ft

40ft

Correct answer:

40ft

Explanation:

Each side would be 10 feet long. A square has 4 sides.

The perimeter of a square is all the sides added together.

P=s_1+s_2+s_3+s_4

Since all the sides are equal in a square we can rewrite the equation to be,

P=4s .

Given

s=10 ,

10 * 4 = 40

Therefore the perimeter is 40ft.

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Example Question #905 : Basic Geometry

If a linoleum tile is a perfect square and has an area of $64\;in^2$ , what is the perimeter of the tile?

Possible Answers:

$32\;in$

$30\;in$

$36\;in$

$28\;in$

$34\;in$

Correct answer:

$32\;in$

Explanation:

Using the formula for area of a square, we can find the length of the sides and solve for the perimeter:

$\\area=length^2\\64\;in^2=length^2\\length=\sqrt{64\;in^2}\\length=8\;in$

Now that we have the length of our sides, we can solve for perimeter:

$\\perimeter=4\cdot length\\perimeter=4\cdot8\;in=32\;in$

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Example Question #501 : Quadrilaterals

If the area of a square is 12.25 square meters, what is its perimeter?

Possible Answers:

37.5 m

24.5 m

14m

3.5 m

Correct answer:

14m

Explanation:

The area of a square is found by squaring the length of each side. That means we can figure out the length of the sides by taking the square root of 12.25. $\sqrt{12.25 } = 3.5$

The length of all 4 sides is 3.5 meters, since this is a square, so the perimeter is $4 \cdot 3.5 = 14 m$

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #491 : Quadrilaterals

Example Question #492 : Quadrilaterals

Example Question #493 : Quadrilaterals

Example Question #494 : Quadrilaterals

Example Question #901 : Plane Geometry

Example Question #61 : How To Find The Perimeter Of A Square

Example Question #62 : How To Find The Perimeter Of A Square

Example Question #61 : How To Find The Perimeter Of A Square

Example Question #905 : Basic Geometry

Example Question #501 : Quadrilaterals

All Basic Geometry Resources

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