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Basic Geometry : Squares

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Example Questions

Example Question #1 : How To Find The Area Of A Square

Point A is the center of the circle.

Figure ABCD is a square.

Segments AB and AD are radii of the circle.

The radius of the circle is units.

Find the area of the green-colored shape.

Possible Answers:

$16 - 4\pi$

$16 - 2\pi$

Correct answer:

$16 - 4\pi$

Explanation:

Square ABCD contains both the red and green shapes. The red shape is equal to the area of one-fourth of the circle. Finding the area of square ABCD and subtracting only the area of the red shape will give the area of only the green shape.

Since ABCD is a square, angle BAC is a right angle that sits at the center of the circle (point A). Since a right angle is 90^o and a circle is 360^o, the red shape's area must be one quarter (or $\frac{1}{4}$ ) of the entire circle's area. Use the equation $A = \pi r^2$ to find the area of the entire circle, then multiply this by $\frac{1}{4}$ to find the area of only the red shape.

$A_{red} = (\pi (4)^2) * (\frac{1}{4})$

$A_{red} = 4\pi$

Subtracting this from the area of the square gives the area of the green area outside of the circle.

$A_{square}=s^2=4^2=16$

$A_{green}=A_{square}-A_{red}$

$A_{green}=16-4\pi$

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Example Question #281 : Quadrilaterals

What is the area of the following square if the length of is $2\sqrt{2}$ ?

Possible Answers:

Correct answer:

Explanation:

We need to find the length of the side of the square in order to find the area. The diagonal makes two $45^{\circ}-45^{\circ}-90^{\circ}$ triangles with the sides of the square. Using the $45^{\circ}-45^{\circ}-90^{\circ}$ special triangle ratio of $n-n-n\sqrt{2}$ , we know that if the hypotenuse is $2\sqrt{2}$ then the length of each side must be . The area of the square is $side^{2} = 2^{^{2}} = 4$ .

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Example Question #31 : Squares

One side of a square is 6 inches long. What is the area of the square in inches?

Possible Answers:

216

2.45

Correct answer:

Explanation:

To find the area of a square, you only need to know one side. The length of one side squared is the area.

$6^{2}=36$

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Example Question #2 : How To Find The Area Of A Square

Side in the square shown below has a length of 13 meters. What is the total area of the square?

Square_diagonal

Possible Answers:

$13\ m^{2}$

$169\ m^{2}$

$26\ m^{2}$

$13\ miles$

$169\ m$

Correct answer:

$169\ m^{2}$

Explanation:

Since the shape in question is a square, we know that is the length of all four sides.

The formula for the area of a square is $area=base\times height$ .

In this case, area = $a\times a$ , or $a^{2}$ . Plug in the given value of a, 13 meters, to solve for the area:

$13^{2}=169$

Remember to use the correct units, in this square meters.

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Example Question #33 : Squares

Find the area of a square that has side lengths of mm.

Possible Answers:

$\sqrt{32}\text{ mm}^2$

$16\text{ mm}^2$

$4\text{ mm}^2$

$20\text{ mm}^2$

$8\text{ mm}^2$

Correct answer:

$16\text{ mm}^2$

Explanation:

The area of any square is: A=s^2 , so

$A=(4)^2=16\, mm^2$

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Example Question #34 : Squares

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.

Possible Answers:

4/7 square units

6/7 square units

1/7 square units

12/14 square units

Correct answer:

6/7 square units

Explanation:

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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Example Question #91 : Quadrilaterals

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

Possible Answers:

$\dpi{100} \small 81$

$\dpi{100} \small 121$

$\dpi{100} \small 100$

$\dpi{100} \small 88$

$\dpi{100} \small 144$

Correct answer:

$\dpi{100} \small 121$

Explanation:

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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Example Question #391 : Act Math

Midpointsquare

Given square ABCD , with midpoints on each side connected to form a new, smaller square. How many times bigger is the area of the larger square than the smaller square?

Possible Answers:

$2\sqrt{2}$

$\sqrt{2}$

$\frac{\sqrt{2}}{2}$

Correct answer:

Explanation:

Assume that the length of each midpoint is 1. This means that the length of each side of the large square is 2, so the area of the larger square is 4 square units. $A=s^{2}$

To find the area of the smaller square, first find the length of each side. Because the length of each midpoint is 1, each side of the smaller square is $\sqrt{2}$ (use either the Pythagorean Theorem or notice that these right trianges are isoceles right trianges, so $s, s, s\sqrt{2}$ can be used).

The area then of the smaller square is 2 square units.

Comparing the area of the two squares, the larger square is 2 times larger than the smaller square.

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Example Question #92 : Quadrilaterals

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

Possible Answers:

4900

140

1225

Correct answer:

1225

Explanation:

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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Example Question #391 : Act Math

Eric has 160 feet of fence for a parking lot he manages. If he is using all of the fencing, what is the area of the lot assuming it is square?

Possible Answers:

$1600\ feet^{2}$

$16,000\ feet^{2}$

$80\ feet^{2}$

$160\ feet^{2}$

$1200\ feet^{2}$

Correct answer:

$1600\ feet^{2}$

Explanation:

The area of a square is equal to its length times its width, so we need to figure out how long each side of the parking lot is. Since a square has four sides we calculate each side by dividing its perimeter by four.

$\frac{160}{4}=40$

Each side of the square lot will use 40 feet of fence.

$Area=length \times width$

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Basic Geometry : Squares

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1 : How To Find The Area Of A Square

Example Question #281 : Quadrilaterals

Example Question #31 : Squares

Example Question #2 : How To Find The Area Of A Square

Example Question #33 : Squares

Example Question #34 : Squares

Example Question #91 : Quadrilaterals

Example Question #391 : Act Math

Example Question #92 : Quadrilaterals

Example Question #391 : Act Math

All Basic Geometry Resources

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