Intermediate Geometry : How to find the area of a parallelogram

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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

The perimeter of a square is .  If the sides of the square are reduced by a factor of two, what is the area of the new square?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a square is geven by  and the area of a square is given by

Thus

so

The original side is reduced by a factor of which results in a new side of .  The area of the new square is geven by

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

Find the area of the box in square inches: 

Geo_box

Possible Answers:

Correct answer:

Explanation:

The answer is .  You can find the area of this box by multiplying the length by its width:

Foil  

 

 If you chose , you added the sides to get the perimeter. 

 

Just remember, the width is 12 added to .  Not 12 times the side of

Example Question #3 : How To Find The Area Of A Parallelogram

If all angles are right angles in the figure below, what is the total area of the figure? 

Box1

Possible Answers:

Correct answer:

Explanation:

The answer is

To get the area, you would need to find the missing sides.  Since the horizontal top is  inches total, the bottom must be  inches total. Thus you would subtract  to get  for the missing bottom horizontal side. 

The vertical right side is  inches total.  Then you would subtract  to get  for the missing vertical side.  

Then you would have to split the figure into 3 different boxes and find the area of each one.  Then you would add the area of each box

Example Question #4 : How To Find The Area Of A Parallelogram

What is the area of a parallelogram if the base is , and the height is ?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a parallelogram is:

So, we are given all of the information that we need to solve this problem. Substitute the provided values into the equation and simplify:

Example Question #5 : How To Find The Area Of A Parallelogram

What is the area of a parallelogram if the base is  and the height is ?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a parallelogram is:

Substitute in the provided values and simplify to calculate the correct answer:

Example Question #6 : How To Find The Area Of A Parallelogram

Find the area of a parallelogram if the base is  and the height is .

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a parallelogram is:

Substitute the values provided in the question:

Use the FOIL method to simplify:

Example Question #7 : How To Find The Area Of A Parallelogram

What is the area of a parallelogram if the base is  and the height is ?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a parallelogram is:

Substitute the values provided in the problem and solve to calculate the correct answer:

Example Question #8 : How To Find The Area Of A Parallelogram

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

1

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

Substitute in the given length and height to find the area of the rectangle.

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

We need to find the height of the parallelogram. From the question, we know the following relationship:

Substitute in the length of the rectangle to find the height of the parallelogram.

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

Solve.

Example Question #51 : Parallelograms

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

2

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

Substitute in the given length and height to find the area of the rectangle.

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

We need to find the height of the parallelogram. From the question, we know the following relationship:

Substitute in the length of the rectangle to find the height of the parallelogram.

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

Solve.

Example Question #10 : How To Find The Area Of A Parallelogram

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

3

Possible Answers:

Correct answer:

Explanation:

13

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

Substitute in the given length and height to find the area of the rectangle.

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

We need to find the height of the parallelogram. From the question, we know the following relationship:

Substitute in the length of the rectangle to find the height of the parallelogram.

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

Solve.

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