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Pre-Algebra/Expressions,Equations,Integers

How to find the perimeter

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