Notes 5.5 – Special Right Triangles and Areas of Regular Polygons

45-45-90 Triangles

These triangles are isosceles right triangles formed by the diagonal of a square.

You can use the Pythagorean Theorem to find the missing sides or use the Theorem.

[THEOREM] In any 45-45-90 right triangle, the length of the hypotenuse is times the length of the leg.

leg

Algebraically (the Mr. Green Method)

Hyp = leg *

Leg = (must be simplified)

30-60-90 Triangles

These triangles are formed by dropping an altitude to the opposite side of an equilateral triangle.

[THEOREM] The length of the hypotenuse is twice the length of the shorter side. The length of the longer side is times the length of the shorter side.

short leg
		long leg = short *

Algebraically (the Mr. Green Method)

You need to find (have) the short leg

Hyp = short * 2

Long = short *

If you need to find the short leg

Short =

Short = (must be simplified)

Area of Regular Polygon

A = ½ aP

a = apothem (altitude), P = perimeter of polygon

OR

You can divide the polygon into triangles

and multiply.