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

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Example Questions

Example Question #2 : Parallelograms

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

Possible Answers:

Correct answer:

Explanation:

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

In this equation, is the length of the base and is the length of the height. We can plug in the side length for both base and height, as given in the question.

A=8*7

A=56

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Example Question #4 : Parallelograms

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

Possible Answers:

Correct answer:

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 A=12*8

Perform the multiplication to arrive at the answer of A=96 .

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Example Question #3 : Parallelograms

Find the area of the following parallelogram:

Screen_shot_2014-02-27_at_6.43.30_pm

Possible Answers:

96m^2

$48\sqrt{3}m^2$

48m^2

Cannot be determined from the given information.

$96\sqrt{3}m^2$

Correct answer:

$48\sqrt{3}m^2$

Explanation:

The formula for the area of a parallelogram is:

A=(b)(h) ,

where is the length of the base and is the length of the height.

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

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

The left side of the parallelogram forms the following 30-60-90 triangle:

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

Plugging in our values, we get:

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

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Example Question #182 : Geometry

Find the area of the following parallelogram:

Screen_shot_2014-03-01_at_9.26.41_pm

Possible Answers:

$144\sqrt{7}m^2$

$54\sqrt{7}m^2$

$36\sqrt{7}m^2$

$45\sqrt{7}m^2$

$72\sqrt{7}m^2$

Correct answer:

$45\sqrt{7}m^2$

Explanation:

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

A^2 + B^2 = C^2

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

B^2 = 175m^2

$B = 5 \sqrt{7}m$

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

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

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

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

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

Find the area of the following parallelogram:

Possible Answers:

$760\ m^2$

$780\ m^2$

$790\ m^2$

$770\ m^2$

$800\ m^2$

Correct answer:

$760\ m^2$

Explanation:

The formula for the area of a parallelogram is

A = (base)(height) .

Use the formula for a 45-45-90 triangle to find the length of the height:

$a-a-a\sqrt{2}$

$4\ m-4\ m-4\sqrt{2}\ m$

Plugging in our values, we get:

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

$A = 760\ m^2$

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

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : Parallelograms

Example Question #4 : Parallelograms

Example Question #3 : Parallelograms

Example Question #182 : Geometry

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

All High School Math Resources

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