High School Math : How to find the area of a parallelogram

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #2 : Parallelograms

What is the area of a parallelogram with a base of \(\displaystyle 8\) and a height of \(\displaystyle 7\)?

 

Possible Answers:

\(\displaystyle 15\)

\(\displaystyle 28\)

\(\displaystyle 56\)

\(\displaystyle 50\)

Correct answer:

\(\displaystyle 56\)

Explanation:

To solve this question you must know the formula for the area of a parallelogram.

In this equation, \(\displaystyle B\) is the length of the base and \(\displaystyle H\) is the length of the height. We can plug in the side length for both base and height, as given in the question.

\(\displaystyle A=8*7\)

\(\displaystyle A=56\)

 

Example Question #3 : Parallelograms

What is the area of a parallelogram with a base of \(\displaystyle 12\) and a height of \(\displaystyle 8\)?

Possible Answers:

\(\displaystyle 84\)

\(\displaystyle 69\)

\(\displaystyle 48\)

\(\displaystyle 96\)

Correct answer:

\(\displaystyle 96\)

Explanation:

To solve this question you must know the formula for the area of a parallelogram.

The formula is 

So we can plug in the side length for both base and height to yield \(\displaystyle A=12*8\)

Perform the multiplication to arrive at the answer of \(\displaystyle A=96\).

Example Question #3 : Parallelograms

Find the area of the following parallelogram:

Screen_shot_2014-02-27_at_6.43.30_pm

Possible Answers:

\(\displaystyle 96m^2\)

\(\displaystyle 48\sqrt{3}m^2\)

\(\displaystyle 48m^2\)

Cannot be determined from the given information.

\(\displaystyle 96\sqrt{3}m^2\)

Correct answer:

\(\displaystyle 48\sqrt{3}m^2\)

Explanation:

The formula for the area of a parallelogram is:

\(\displaystyle A=(b)(h)\),

where \(\displaystyle b\) is the length of the base and \(\displaystyle h\) is the length of the height.

 

In order to the find the height of the parallelogram, use the formula for a \(\displaystyle 30-60-90\) triangle:

\(\displaystyle a-a\sqrt{3}-2a\), where \(\displaystyle a\) is the side opposite the \(\displaystyle \measuredangle30\).

The left side of the parallelogram forms the following \(\displaystyle 30-60-90\) triangle:

\(\displaystyle 4m-4\sqrt{3}m-8m\), where \(\displaystyle 4\sqrt{3}m\) is the length of the height.

 

Plugging in our values, we get:

\(\displaystyle A=(12m)(4\sqrt{3}m)=48\sqrt{3}m^2\)

Example Question #182 : Geometry

Find the area of the following parallelogram:

Screen_shot_2014-03-01_at_9.26.41_pm

Possible Answers:

\(\displaystyle 144\sqrt{7}m^2\)

\(\displaystyle 54\sqrt{7}m^2\)

\(\displaystyle 36\sqrt{7}m^2\)

\(\displaystyle 45\sqrt{7}m^2\)

\(\displaystyle 72\sqrt{7}m^2\)

Correct answer:

\(\displaystyle 45\sqrt{7}m^2\)

Explanation:

Use the Pythagorean Theorem to determine the length of the diagonal:

\(\displaystyle A^2 + B^2 = C^2\)

\(\displaystyle (9m)^2 + B^2 = (16m^2)\)

\(\displaystyle B^2 = 175m^2\)

\(\displaystyle B = 5 \sqrt{7}m\)

 

The area of the parallelogram is twice the area of the right triangles:

\(\displaystyle A_{Triangle} = \frac{1}{2} (b)(h)\)

\(\displaystyle A_{Triangle} = \frac{1}{2} (9m)(5m\sqrt{7}) = \frac{45m^2\sqrt{7}}{2}\)

\(\displaystyle A_{Parallelogram} = 2 (A_{Triangle}) = 2\left(\frac{45m^2\sqrt{7}}{2}\right)=45m^2\sqrt{7}\)

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

Find the area of the following parallelogram:

18

Possible Answers:

\(\displaystyle 760\ m^2\)

\(\displaystyle 790\ m^2\)

\(\displaystyle 800\ m^2\)

\(\displaystyle 770\ m^2\)

 

 

\(\displaystyle 780\ m^2\)

Correct answer:

\(\displaystyle 760\ m^2\)

Explanation:

The formula for the area of a parallelogram is

\(\displaystyle A = (base)(height)\).

Use the formula for a \(\displaystyle 45-45-90\) triangle to find the length of the height:

\(\displaystyle a-a-a\sqrt{2}\)

\(\displaystyle 4\ m-4\ m-4\sqrt{2}\ m\)

Plugging in our values, we get:

\(\displaystyle A = (19\ m)(4\ m)\)

\(\displaystyle A = 760\ m^2\)

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