Pre-Algebra : Area of a Parallelogram

Example Questions

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Example Question #1 : Area Of A Parallelogram

What is the area of the parallelogram?

Explanation:

The area of a parallelogram is determined using the equation:

In this problem:

Example Question #2 : Area Of A Parallelogram

Refer to the above figure, which shows Parallelogram . You are given that  and

If you know the length of , then, of the following segments, choose the one whose length, if known, will allow us to calculate the area of Parallelogram  .

Explanation:

The area of a parallelogram is the product of the length of any one side, or its base, and the perpendicular distance to the opposite side, or its height. If we know , then we also know , which is of the same length. We can take  to be the base, and the segement perpendicular to it, , as the altitude. Therefore,  is the segment whose length we need to know.

Example Question #3 : Area Of A Parallelogram

Note: Figure NOT drawn to scale.

Refer to the above figure, which shows Parallelogram . You are given that  and

Evaluate .

Explanation:

The area of a parallelogram is the product of the length of any one side, or its base, and the length of a segment perpendicular to that side, or its height.

One way to find the area is to multiply the length of side  by its corresponding altitude, . Since  and

.

Another way to find the area is to multiply the length of side  by its corresponding altitude, . Since  and the area is 9,600, we set up this equation and solve for :

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

A parallelogram has the base length of and the altitude of . Give the area of the parallelogram.

Explanation:

The area of a parallelogram is given by:

Where is the base length and is the corresponding altitude. So we can write:

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

A parallelogram has a base length of  which is 3 times longer than its corresponding altitude. The area of the parallelogram is 12 square inches. Give the .

Explanation:

Base length is so the corresponding altitude is  .

The area of a parallelogram is given by:

Where:

is the length of any base
is the corresponding altitude

So we can write:

Example Question #1 : Area Of A Parallelogram

The length of the shorter diagonal of a rhombus is 40% that of the longer diagonal. The area of the rhombus is . Give the length of the longer diagonal in terms of .

Explanation:

Let  be the length of the longer diagonal. Then the shorter diagonal has length 40% of this. Since 40% is equal to , 40% of  is equal to .

The area of a rhombus is half the product of the lengths of its diagonals, so we can set up, and solve for , in the equation:

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

The length of the shorter diagonal of a rhombus is two-thirds that of the longer diagonal. The area of the rhombus is  square yards. Give the length of the longer diagonal, in inches, in terms of .

Explanation:

Let  be the length of the longer diagonal in yards. Then the shorter diagonal has length two-thirds of this, or .

The area of a rhombus is half the product of the lengths of its diagonals, so we can set up the following equation and solve for :

To convert yards to inches, multiply by 36:

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

The longer diagonal of a rhombus is 20% longer than the shorter diagonal; the rhombus has area . Give the length of the shorter diagonal in terms of .

Explanation:

Let  be the length of the shorter diagonal. If the longer diagonal is 20% longer, then it measures 120% of the length of the shorter diagonal; this is

of , or .

The area of a rhombus is half the product of the lengths of its diagonals, so we can set up an equation and solve for :

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

Find the area:

Explanation:

The area of a parallelogram can be determined using the following equation:

Therefore,

Example Question #3 : Area Of A Parallelogram

Find the area of a parallelogram with a base of length 8 and a height of length 6.