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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
16 + 8√3 units this is your final answer because you can't add a constant and a radical
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.