Math - How to find the perimeter of a parallelogram

Find the perimeter of the following parallelogram:

$38 + 8\sqrt{2}\ m$

$36 + 8\sqrt{2}\ m$

$34 + 8\sqrt{2}\ m$

$32 + 8\sqrt{2}\ m$

$40 + 8\sqrt{2}\ m$

Explanation

The formula for the perimeter of a parallelogram is

Plugging in our values, we get:

$P = 2(4\sqrt{2}\ m)+2(19\ m)$

$P = 38 + 8\sqrt{2}\ m$

Find the perimeter of the following parallelogram:

Screen_shot_2014-02-27_at_6.43.30_pm

Explanation

The formula for the perimeter of a trapezoid is:

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

Opposite sides of a parallelogram have the same length. Therefore, both edges are and both bases are .

Plugging in our values, we get:

Find the perimeter of the following parallelogram:

Screen_shot_2014-03-01_at_9.26.41_pm

Explanation

The formula for the perimeter of a parallelogram is:

$P = 2(s_{long}) + 2(s_{short})$

where $s_{long}$ is the length of the longer side and $s_{short}$ is the length of the shorter side.

Plugging in our values, we get:

A parallelogram, with dimensions in cm, is shown below. Act1

What is the perimeter of the parallelogram, in cm?

$64+12\sqrt{3}$

Explanation

The triangle on the left side of the figure has a $30^{\circ}$ and a $90^{\circ}$ angle. Since all of the angles of a triangle must add up to $180^{\circ}$ , we can find the angle measure of the third angle:

$180-120=60^{\circ}$

Our third angle is $60^{\circ}$ and we have a triangle.

A triangle has sides that are in the corresponding ratio of $x-x\sqrt{3}-2x$ . In this case, the side opposite our $30^{\circ}$ angle is , so

We also now know that

$x\sqrt{3}=6\sqrt{3}$

Now we know all of our missing side lengths. The right and left side of the parallelogram will each be . The bottom and top will each be $20+6\sqrt{3}$ . Let's combine them to find the perimeter: