How to find the area of a parallelogram

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Math › How to find the area of a parallelogram

Questions 1 - 5

1

Find the area of the following parallelogram:

$760\ m^2$

$770\ m^2$

$780\ m^2$

$790\ m^2$

$800\ m^2$

Explanation

The formula for the area of a parallelogram is

.

Use the formula for a 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:

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

$A = 760\ m^2$

2

Find the area of the following parallelogram:

Screen_shot_2014-02-27_at_6.43.30_pm

$48\sqrt{3}m^2$

$96\sqrt{3}m^2$

Cannot be determined from the given information.

Explanation

The formula for the area of a parallelogram is:

,

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 triangle:

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

The left side of the parallelogram forms the following triangle:

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

Plugging in our values, we get:

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

3

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

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.

4

Find the area of the following parallelogram:

Screen_shot_2014-03-01_at_9.26.41_pm

$45\sqrt{7}m^2$

$54\sqrt{7}m^2$

$144\sqrt{7}m^2$

$36\sqrt{7}m^2$

$72\sqrt{7}m^2$

Explanation

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

$B = 5 \sqrt{7}m$

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

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

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

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

5

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

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

Perform the multiplication to arrive at the answer of .

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