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Basic Geometry : Rectangles

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Example Questions

Example Question #85 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

152.42

150.64

153.06

151.37

Correct answer:

153.06

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{16}{2}$

$\text{radius}=8$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times8^2$

$\text{Area of circle}=64\pi$

Next, find the area of the rectangle.

$\text{Area of rectangle}=\text{length}\times\text{width}$

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=4\times 12$

$\text{Area of rectangle}=48$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=64\pi - 48$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=153.06$

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Example Question #86 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

171.15

174.47

176.69

171.29

Correct answer:

174.47

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

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

$\text{radius}=9$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times9^2$

$\text{Area of circle}=81\pi$

Next, find the area of the rectangle.

$\text{Area of rectangle}=\text{length}\times\text{width}$

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=5\times 16$

$\text{Area of rectangle}=80$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=81\pi - 80$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=174.47$

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Example Question #641 : Basic Geometry

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

239.80

232.32

210.61

236.16

Correct answer:

236.16

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{20}{2}$

$\text{radius}=10$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times10^2$

$\text{Area of circle}=100\pi$

Next, find the area of the rectangle.

$\text{Area of rectangle}=\text{length}\times\text{width}$

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=6\times 13$

$\text{Area of rectangle}=78$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=100\pi - 78$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=236.16$

Report an Error

Example Question #88 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

320.38

327.41

326.39

328.51

Correct answer:

326.39

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{24}{2}$

$\text{radius}=12$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times12^2$

$\text{Area of circle}=144\pi$

Next, find the area of the rectangle.

$\text{Area of rectangle}=\text{length}\times\text{width}$

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=9\times 14$

$\text{Area of rectangle}=126$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=144\pi - 126$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=326.39$

Report an Error

Example Question #89 : How To Find The Area Of A Rectangle

A rectangle is placed inside a circle as shown in the figure.

If the diameter of the circle is , what is the area of the shaded region?

Possible Answers:

491.39

492.25

490.75

489.51

Correct answer:

492.25

Explanation:

In order to find the area of the shaded region, you must subtract the area of the rectangle from the area of the circle.

First, let's find the area of the circle.

Recall how to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{radius}=\frac{\text{Diameter}}{2}$

Substitute in the length of the diameter to find the length of the radius.

$\text{radius}=\frac{32}{2}$

$\text{radius}=16$

Now, use the radius to find the area of the circle.

$\text{Area of circle}=\pi\times16^2$

$\text{Area of circle}=256\pi$

Next, find the area of the rectangle.

$\text{Area of rectangle}=\text{length}\times\text{width}$

Substitute in the given values for the length and the width.

$\text{Area of rectangle}=12\times 26$

$\text{Area of rectangle}=312$

Now that we have both areas, we can find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of circle}-\text{Area of rectangle}$

$\text{Area of shaded region}=256\pi - 312$

Solve and round the answer to two decimal places.

$\text{Area of shaded region}=492.25$

Report an Error

Example Question #90 : How To Find The Area Of A Rectangle

Rectangle 1

Find the area of the rectangle.

Possible Answers:

$\frac{13}{4}$

Correct answer:

Explanation:

To find the area of any rectangle, multiply the base and height.

Use this formula:

A=b*h .

In this case, the base is and the height is .

When we multiply 13*4 , the answer is , so that is the area of the rectangle.

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Example Question #91 : How To Find The Area Of A Rectangle

Rec 2

If x=7 , find the area of the rectangle.

Possible Answers:

108

Correct answer:

Explanation:

To find the area of the rectangle, use the formula

A=b*h .

In this case the base of the rectangle is , because the base is

2x=2(7) .

Since the height is , the height is .

Now that we know the base is and the height is , multiply these two numbers together to get a final area of .

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Example Question #92 : How To Find The Area Of A Rectangle

Rec 3

If the area of the above rectangle is 27, find the value of .

Possible Answers:

Too little information to determine.

s=2.66

s=5

s=9

s=3

Correct answer:

s=3

Explanation:

To find the value of the side of a rectangle, first think about the area 27, in terms of the formula used to find the area of a rectangle.

The area of a rectangle can be found with the equation:

A=b*h .

In terms of our problem, this means that

A=3s*s ,

A=3s^2 .

Now, plug 27 into this equation and work backwards to solve for s algebraically:

I. 27=3s^2

II. 9=s^2

III. s=3

Therefore, the value of s is 3.

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Example Question #231 : Rectangles

Rec 4

Find the area of the above rectangle.

Possible Answers:

Correct answer:

Explanation:

To find the area of the rectangle, use the formula

A=b*h .

In this case, the base is 8 and the height is 1/2.

Although the 1/2 is a fraction, it is still a measurement and therefore we just multiply the two numbers.

The answer is 4 because

$8\left(\frac{1}{2}\right)=4$ .

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Example Question #91 : How To Find The Area Of A Rectangle

Rec 5

Find the area of the rectangle in terms of variables.

Possible Answers:

0.5x^2

1.5x

1.5x^2

Correct answer:

0.5x^2

Explanation:

Although we are not finding a whole number solution, we can still use the same formula to find the area of the rectangle.

That formula is

A=b*h .

In this case, the base is and the height is 0.5x .

Therefore, to find the area, we multiply these two sides to get a final area of 0.5x^2 .

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Basic Geometry : Rectangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #85 : How To Find The Area Of A Rectangle

Example Question #86 : How To Find The Area Of A Rectangle

Example Question #641 : Basic Geometry

Example Question #88 : How To Find The Area Of A Rectangle

Example Question #89 : How To Find The Area Of A Rectangle

Example Question #90 : How To Find The Area Of A Rectangle

Example Question #91 : How To Find The Area Of A Rectangle

Example Question #92 : How To Find The Area Of A Rectangle

Example Question #231 : Rectangles

Example Question #91 : How To Find The Area Of A Rectangle

All Basic Geometry Resources

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