Quick Math Homework Help

# How to find the perimeter of a parallelogram

Problem 1 Find the perimeter of a parallelogram with a side of 3 units and 10 units.

Step 1. The opposite sides of a parallelogram are congruent. Therefore, if you know the length of one side you know the length of the other.

Step 2. Add all four sides 3+3+10+10=26 units or (2*3) + (2*10) = 6+20=26 units

Problem 2 Find the perimeter of a parallelogram with a side of 8 units and a height of 6 units and an angle measure of 60 degrees.

Step 1 Use the altitude to find the length of the missing side.

Step 2 The altitude creates a 30-60-90 triangle. If you find the hypothesis of the 30-60-90 Triangle this will be the length of the missing side.

Step 3 The height becomes the long leg which equals x√(3 )
See the 30-60-90 triangle above

Parallelogram height = triangle long leg = 6, now find the short leg  and the hypotenuse (which is the missing side of the parallelogram).

Step 4. Now that you know x, or the short leg, you can multiple x by 2 to find the hypotenuse
2*2√3  =4√3

Step 5. Now use the perimeter formula for a parallelogram 2l + 2w

2*8 + 2*4√3

There are two methods for finding the perimeter of a parallelogram

Method 1 Find the Perimeter of a Parallelogram by adding all four sides​

Method 2 Perimeter of parallelogram equals 2 l +2w
l = length  w = width

## What is a parallelogram?

A parallelogram is a four sided polygon in which both pairs of opposite sides are parallel

As a result a parallelogram has these properties
• Congruent opposite sides AB≌DC
• Congruent opposite angles <A≌<C ,  <D≌<B
• Supplementary consecutive angles <A+<B = 180° <C+<D =180° <D+<A =180° <B + <C = 180°
6
8
8
6
3
Rationalize the denominators
• The diagonals bisect each other AE ≌ EC DE ≌ EB
• Two congruent triangles are created by the diagonals

Common Core Standard:  G.GPE.7
What is perimeter?  Perimeter is the distance around an object. If you measure the distance around a 2 dimensional shape, you have measured the perimeter.
The word perimeter is a combination of the Greek word peri which means around, and meter which is the unit of measure for distance.

## Perimeter of parallelogram problems

Quick summary perimeter of parallelogram problems

Perimeter Problem 1. The length of two sides was given, therefore perimeter could be calculated by adding the length of the four sides.  Because opposite sides of a parallelogram are equal, you could also use 2 x length + 2 x width.

Perimeter Problem 2. Only the length of one side was given. As a result you had to find one missing side of the parallelogram. Because of the properties of a parallelogram, the altitude can be used to find the missing side. The altitude creates a 30 60 90 triangle,and the hypotenuse is your missing side.