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Basic Geometry : Squares

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #251 : Squares

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 $\displaystyle 50ft$

40ft $\displaystyle 40ft$

20ft $\displaystyle 20ft$

30ft $\displaystyle 30ft$

10ft $\displaystyle 10ft$

Correct answer:

40ft $\displaystyle 40ft$

Explanation:

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

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

$\displaystyle P=s_1+s_2+s_3+s_4$

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

P=4s $\displaystyle P=4s$.

Given

s=10 $\displaystyle s=10$,

$\displaystyle 10 * 4 = 40$

Therefore the perimeter is 40ft.

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Example Question #251 : Squares

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

Possible Answers:

$34\;in$ $\displaystyle 34\;in$

$32\;in$ $\displaystyle 32\;in$

$30\;in$ $\displaystyle 30\;in$

$28\;in$ $\displaystyle 28\;in$

$36\;in$ $\displaystyle 36\;in$

Correct answer:

$32\;in$ $\displaystyle 32\;in$

Explanation:

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

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

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

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

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Example Question #251 : Squares

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

Possible Answers:

37.5 m $\displaystyle 37.5 m$

3.5 m $\displaystyle 3.5 m$

14m $\displaystyle 14m$

24.5 m $\displaystyle 24.5 m$

Correct answer:

14m $\displaystyle 14m$

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. $\sqrt{12.25 } = 3.5$ $\displaystyle \sqrt{12.25 } = 3.5$

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

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Example Question #65 : How To Find The Perimeter Of A Square

Square abcd

In square ABCD, the length of line BC is $2\sqrt{2}$ $\displaystyle 2\sqrt{2}$ inches. What is the perimeter of square ABCD?

Possible Answers:

$8\sqrt{2}\ in$ $\displaystyle 8\sqrt{2}\ in$

$6\ in$ $\displaystyle 6\ in$

$1\ ft$ $\displaystyle 1\ ft$

$10\ in$ $\displaystyle 10\ in$

$8\ in$ $\displaystyle 8\ in$

Correct answer:

$8\ in$ $\displaystyle 8\ in$

Explanation:

In any square, the diagonal (BC) will always be equal to the length of any side multiplied by √2.

So, if the diagonal is equal to 2√2, then working backwards, you have to divide the diagonal length by √2.

Screen shot 2015 11 30 at 11.55.30 am

So if the diagonal is equal to 2√2, then any given side should equal 2.

If you add up all the sides, your final answer is 8.

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Example Question #252 : Squares

Find the perimeter, $\displaystyle P$, of a square whose side length, $\displaystyle b$, is 7.9.

Possible Answers:

P=31.6 $\displaystyle P=31.6$

P=30 $\displaystyle P=30$

P=29 $\displaystyle P=29$

P=62.41 $\displaystyle P=62.41$

Correct answer:

P=31.6 $\displaystyle P=31.6$

Explanation:

The formula for the perimeter of a square is

P=4b $\displaystyle P=4b$.

$\displaystyle P=4b=4*7.9=31.6$

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Example Question #253 : Squares

Know that in a Major League Baseball infield the distance between home plate and first base is 90 feet and the infield is a perfect square.

How many feet does a batter run when they hit a home run?

Possible Answers:

$100\ ft$ $\displaystyle 100\ ft$

$900\ ft$ $\displaystyle 900\ ft$

$300\ ft$ $\displaystyle 300\ ft$

$90\ ft$ $\displaystyle 90\ ft$

$360\ ft$ $\displaystyle 360\ ft$

Correct answer:

$360\ ft$ $\displaystyle 360\ ft$

Explanation:

Because the baserunner is going in a perfect square, they run 90 feet four different times.

We can solve the total distance with the equation

$90\times4=360.$ $\displaystyle 90\times4=360.$

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Example Question #68 : How To Find The Perimeter Of A Square

Know that in a Major League Baseball infield the distance between home plate and first base is 90 feet and the infield is a perfect square.

If a baserunner is standing on second base and their teammate hits a home run, how far does the baserunner run to reach home plate?

Possible Answers:

$270\ ft$ $\displaystyle 270\ ft$

$500\ ft$ $\displaystyle 500\ ft$

$90\ ft^2$ $\displaystyle 90\ ft^2$

$360\ ft$ $\displaystyle 360\ ft$

$180\ ft$ $\displaystyle 180\ ft$

Correct answer:

$180\ ft$ $\displaystyle 180\ ft$

Explanation:

Because the baserunner is on second base, they only have to run from second base to third base and third base to home plate.

This means they run the length of two sides of the square.

So, they run

$90 + 90 = 180\ ft$ $\displaystyle 90 + 90 = 180\ ft$.

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Example Question #69 : How To Find The Perimeter Of A Square

Know that in a Major League Baseball infield the distance between home plate and first base is 90 feet and the infield is a perfect square.

If a batter is hits a triple and makes it all the way to third base how far did they run?

Possible Answers:

$300\ ft$ $\displaystyle 300\ ft$

$90\ ft$ $\displaystyle 90\ ft$

$1200\ ft$ $\displaystyle 1200\ ft$

$270\ ft$ $\displaystyle 270\ ft$

$360\ ft$ $\displaystyle 360\ ft$

Correct answer:

$270\ ft$ $\displaystyle 270\ ft$

Explanation:

The batter runs from home plate to first base, first base to second base, and second base to third base.

That means they run three sides of the square infield.

So they ran 90 Feet three times.

$90 + 90 + 90 = 270\ ft$ $\displaystyle 90 + 90 + 90 = 270\ ft$

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Example Question #913 : Basic Geometry

Know that in a Major League Baseball infield the distance between home plate and first base is 90 feet and the infield is a perfect square.

If a batter ran to first, then started to run toward second base, but decided to go back to first base when they were halfway to second, how far would they have run in total by the time the made it back to first base?

Possible Answers:

$45\ ft$ $\displaystyle 45\ ft$

$270\ ft$ $\displaystyle 270\ ft$

$90\ ft$ $\displaystyle 90\ ft$

$120\ ft$ $\displaystyle 120\ ft$

$180\ ft$ $\displaystyle 180\ ft$

Correct answer:

$180\ ft$ $\displaystyle 180\ ft$

Explanation:

If they run this way they run 90 feet between home plate and first base, 45 feet between first base and the point where they turn around, and 45 more feet from where they turned around to first base. So, they ran

$90 + 45 + 45 = 180\ ft$ $\displaystyle 90 + 45 + 45 = 180\ ft$

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Example Question #914 : Basic Geometry

Know that in a Major League Baseball infield the distance between home plate and first base is 90 feet and the infield is a perfect square.

If a baserunner is on third base and the batter hits a home run, how far to the two players run in total?

Possible Answers:

$900\ ft$ $\displaystyle 900\ ft$

$450\ ft$ $\displaystyle 450\ ft$

$90\ ft$ $\displaystyle 90\ ft$

$540\ ft$ $\displaystyle 540\ ft$

$360\ ft$ $\displaystyle 360\ ft$

Correct answer:

$450\ ft$ $\displaystyle 450\ ft$

Explanation:

The baserunner on third base runs 90 feet to home plate and is done running.

The batter who hit the home run runs all four sides of the square, so they run 360 feet.

$360 + 90 = 450\ ft$ $\displaystyle 360 + 90 = 450\ ft$

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Basic Geometry : Squares

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #251 : Squares

Example Question #251 : Squares

Example Question #251 : Squares

Example Question #65 : How To Find The Perimeter Of A Square

Example Question #252 : Squares

Example Question #253 : Squares

Example Question #68 : How To Find The Perimeter Of A Square

Example Question #69 : How To Find The Perimeter Of A Square

Example Question #913 : Basic Geometry

Example Question #914 : Basic Geometry

All Basic Geometry Resources

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