Squares - Geometry

Card 0 of 1304

Question

A square has one side of length , what is the length of the opposite side?

Answer

One of the necessary conditions of a square is that all sides be of equal length. Therefore, because we are given the length of one side we know the length of all sides and that includes the length of the opposite side. Since the length of one of the sides is 4 we can conclude that all of the sides are 4, meaning the opposite side has a length of 4.

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Question

Find the side length of a square given the area is 144.

Answer

To solve, simply use the formula for the area of a square to solve for side length. Thus,

$A=s^2\Rightarrow s=\sqrt{A}$

$s=\sqrt{144}=12$

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Question

The diagonal of a square has a length of 10 inches. What is the perimeter of the square in inches squared?

Answer

Using the Pythagorean Theorem, we can find the edge of a side to be √50, by 2a2=102. This can be reduced to 5√2. This can then be multiplied by 4 to find the perimeter.

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Question

A square garden has an area of 64 square feet. If you add 3 feet to each side, what is the new perimeter of the garden?

Answer

By finding the square root of the area of the garden, you find the length of one side, which is 8. We add 3 feet to this, giving us 11, then multiply this by 4 to get 44 feet for the perimeter.

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Question

Find the perimeter of a square that has side lengths of .

Answer

Use the following formula to find the perimeter of a square:

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

For the given square,

$\text{Perimeter}=4(2.5)=10$

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Question

Find the perimeter of a square that has side lengths .

Answer

Use the following formula to find the perimeter of a square:

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

For the given square,

$\text{Perimeter}=4(6.3)=25.2$

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Question

Find the perimeter of a square that has side lengths of .

Answer

Use the following formula to find the perimeter of a square:

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

For the given square,

$\text{Perimeter}=4(12.6)=50.4$

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Question

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

Answer

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

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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Question

Find the perimeter, , of a square whose side length, , is 7.9.

Answer

The formula for the perimeter of a square is

.

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Question

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

Answer

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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Question

A square is circumscribed on a circle with a 6 inch radius. What is the area of the square, in square inches?

Answer

We know that the radius of the circle is also half the length of the side of the square; therefore, we also know that the length of each side of the square is 12 inches.

We need to square this number to find the area of the square.

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Question

A square garden has sides that are feet long. In square feet, what is the area of the garden?

Answer

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=8^2=64$

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Question

In square meters, find the area of a square that has a side length of meter.

Answer

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=1^2=1$

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Question

Jennifer wants to put down carpet on her bedroom floor that is a square with side lengths of feet. In square feet, how much carpet is needed?

Answer

Use the following formula to find the area of a square:

$\text{Area}=(\text{side length})^2$

For the given square,

$\text{Area}=14^2=196$

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Question

Find the area of the square.

Answer

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.

$\text{Area}=1682$

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Question

Find the area of a square given side length of 4.

Answer

To find the area of a square multiply the width with the length. In the case of a square, all sides are the same length thus, the area is simply the side length squarred.

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

.

Thus,

.

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Question

How much more area does a square with a side of 2r have than a circle with a radius r? Approximate π by using 22/7.

Answer

The area of a circle is given by A = πr2 or 22/7r2

The area of a square is given by A = s2 or (2r)2 = 4r2

Then subtract the area of the circle from the area of the square and get 6/7 square units.

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Question

If a completely fenced-in square-shaped yard requires 140 feet of fence, what is the area, in square feet, of the lot?

Answer

Since the yard is square in shape, we can divide the perimeter(140ft) by 4, giving us 35ft for each side. We then square 35 to give us the area, 1225 feet.

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Question

If the perimeter of a square is 44 centimeters, what is the area of the square in square centimeters?

Answer

Since the square's perimeter is 44, then each side is $\dpi{100} \small \frac{44}{4}=11$ .

Then in order to find the area, use the definition that the

$\dpi{100} \small Area=side^{2}$

$\dpi{100} \small 11^{2}=121$

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Question

Find the area of a square if it has a diagonal of $3\sqrt2$ .

Answer

The diagonal of a square is also the hypotenuse of a triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

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

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

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

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

Substitute in the length of the diagonal to find the area of the square.

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

Simplify.

$\text{Area}=\frac{18}{2}$

$\text{Area}=9$

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