# How to find the perimeter

**Problem 1** *What is the perimeter of a square that has a side of 8 units?*

Use the formula 4 * side

4*8 =32 units

**Problem 1****.*** What is the perimeter of a trapezoid that has sides of 4, 5, 6, and 8 units in length? *

Perimeter = Add the length of all four sides

4 + 5 + 6 + 8 = 23 units

**Problem 2**. *Find the perimeter of an isosceles triangle that has sides of 5, 4, and 8 units in length?*

## Equilateral Triangle, Square, Trapezoid

**Step 3.** Plug the length of 1 side into the "Perimeter Formula" 4*s

**Problem 2** *What is the perimeter of a square in which you only know the diagonal length of 10 units?*

**Step 1.** Inside a square you have a 45-45-90 right triangle.

Side length of a 45 45 90 triangle = Hypotenuse ÷ √2

Hypotenuse = Side length *√2

**Step 2.** Plug the hypotenuse length into " Hypotenuse ÷ √2 "

**Problem 1.** *What is the perimeter measure of an equilateral triangle that has a side measure of 4 units?*

**Step 1.** We will use the formula 3s (s= to one side length)

**Step 2.** 3 x 4=12 units

**Problem 2.** This one is a little more challenging.

What is the perimeter measure of an equilateral triangle with a height of 6 units?

**Step 1**. The height measure cuts the equilateral triangle into two 30-60-90 triangles.

The altitude ( height) becomes the long leg of the 30 60 90 triangle and can be used to find the side length of the square.

**Step 2.** The short leg = long leg /√3 6/√3

Rationalize = 6/√3 = √3/√3 = 6√3/3= 2√3

**Step 3**. Now we have half the distance of one side. The whole length equals 2x2√3=4√3

**Step 4.** Apply the perimeter formula of 3 * side

3*4√3 =12√(3 ) units equals the perimeter of the square

*The video above works out this problem*

In a 30 60 90 triangle:

hypotenuse = 2 * short leg

short leg = hypotenuse ÷ 2

long leg = short leg * √3

**Step 1.** An isosceles trapezoid has two parallel sides and two non-parallel sides of equal length.

The missing side will be 5 units because it is a non-parallel side and non-parallel sides are congruent. .

**Step 2**.Add the length of the four sides.

5 + 5 + 8 + 4 = 22 units = the perimeter