Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #641 : Basic Geometry

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

8

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

Possible Answers:

Correct answer:

Explanation:

13

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:

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

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

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

Next, find the area of the rectangle.

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

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

Solve and round the answer to two decimal places.

Example Question #82 : How To Find The Area Of A Rectangle

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

10

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

Possible Answers:

Correct answer:

Explanation:

13

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:

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

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

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

Next, find the area of the rectangle.

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

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

Solve and round the answer to two decimal places.

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

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

12

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

Possible Answers:

Correct answer:

Explanation:

13

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:

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

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

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

Next, find the area of the rectangle.

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

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

Solve and round the answer to two decimal places.

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

Rectangle 1

Find the area of the rectangle.

Possible Answers:

Correct answer:

Explanation:

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

Use this formula: 

.  

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

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

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

Rec 2

If , find the area of the rectangle.

Possible Answers:

Correct answer:

Explanation:

To find the area of the rectangle, use the formula 

.  

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

.  

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 .

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.

Correct answer:

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: 

.  

In terms of our problem, this means that 

,

or 

.  

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

I. 

II. 

III. 

Therefore, the value of s is 3.

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 

.  

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 

.

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:

Correct answer:

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 

.  

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

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

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

Rec 6

Find the area of the above rectangle and include units in your answer.

Possible Answers:

Correct answer:

Explanation:

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

Use this formula: 

.  

In this case, the base is 8 and the height is 3.  

When we multiply 8 by 3, the answer is 24, so that is the area of the rectangle.  

The unit of each side is centimeters, so when you multiply them together, the unit of area is centimeters squared.

Example Question #641 : Plane Geometry

Rec 7 

Find the area of the rectangle.

Possible Answers:

Correct answer:

Explanation:

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

Use this formula: 

.  

In this case, the base is 42 and the height is 89.  

When we multiply 42 by 89, the answer is 3738, so that is the area of the rectangle.

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