  Master the 7 pillars of school success         # 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

​  = Perimeter

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 2Find 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 " 30
60
90
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