**Perimeter of a Parallelogram**

Watch the video to see each problem worked out

In order to find the perimeter of a parallelogram you can use two methods.

**Method 1** Perimeter of parallelogram equals, add all four sides

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

**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 ) x = the length of the short leg

Since you know the length of the long leg you can use 6=x√3

**Step 3A** 6/√3 = √3/√3

**Step 3B** (6√3)/2 =2√3

**Step 4 **Now that I know x I can use 2x 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 this is your final answer because you can add a constant and a radical

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