1. Please work on the pink warm up

2. 5.5 Special Triangles & Areas of Regular Polygons

3. There are 2 special right triangles 45-45-90 30-60-90
In a triangle, the length of the hypotenuse is 2 times the length of the shorter leg AND the length of the longer leg is √3 times the length of the shorter leg.
In a triangle, the length of the hypotenuse is √2 times the length of the leg. x
x √3 2x
x √2 x
FIND THE SHORT LEG FIRST!!!

4. LET’S TRY THIS… Short side first!! X = 6 Y = _____ Z = _____
6 √3 12 Z 60 X
2 √3
X = _______ Y = Z = ________
4 √3 30
Short side first!! Y P Q R
4 √2 8
P = ______ Q = 4√2 R= _____ 5
5√2
P = Q = ________ R = ________

5. Find the area game♥ A = ½ bh What is the length of the missing side? 6
A = 18 sq. units 6 10
A = ½ bh Find the short side first!!
A = ½ (5) (5√3)
Find an exact answer
A = 25√3 sq. units or √3 2
5√3 5

6. Areas of Regular Polygons
What part of A=1/2bh is the perpendicular bisector?
Can you find the area of a triangle?
The perpendicular bisector of a triangle in a polygon is called an APOTHEM.
The formula for the area of a regular polygon is:
A = ½ap
a is the length of the apothem
p is the perimeter of the polygon

7. Let’s see how this works…10
A = 1/2ap
A = ½(6.88)(50)
A = 172 sq.units
6.88
PAINLESS!!
Let’s kick it up a notch…

8. Find the area of this one!
Hmmmmm….. A circle has 360°… 12
Hmmmmm….. How many degrees would the top angle of each Δ have?
60°
Hmmmmm….. Since the Δs are isosceles, what are the measures of the base angles?
30°
60°
Hmmmmm….. If the apothem is an angle bisector, then what is the measure of the small top angle?
30°
60°
The short side = 6
The apothem = 6√3
A = 1/2ap
A = ½(6√3)(72) = 216√3 (exact)
A = (approx.)

9. WHEW! Try this…
Find the perimeter and area of a Δ with a hypotenuse of 18units.
(sketch it)
What is the length of the short side?
What is the length of the long leg?
What is the perimeter? (exact)
27 + 9√3 units
What is the area? (exact)
81√3 sq units or √3 units2 2 18
60° 9
30°
9√3
(hint: the smallest angle is across from the smallest side… the largest angle is across from the largest side.)

10. Whiteboard time!!

11. Assignment pg 336, 10-21