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Please work on the pink warm up

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5.5 Special Triangles & Areas of Regular Polygons

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There are 2 special right triangles In a triangle, the length of the hypotenuse is 2 times the length of the leg. x 2 x x 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. FIND THE SHORT LEG FIRST!!! x x 3 2x

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LETS TRY THIS… X = 6 Y = _____ Z = _____ X Y Z X = _______ Y = 6 Z = ________ Short side first!! P = ______ Q = 42 R= _____ P = 5 Q = ________ R = ________ P Q R

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Find the area game A = ½ bh What is the length of the missing side? 6 A = ½ (6) (6) A = 18 sq. units 10 A = ½ bh Find the short side first!! A = ½ (5) (53) Find an exact answer A = 253 sq. units or

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Areas of Regular Polygons 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 Can you find the area of a triangle? What part of A=1/2bh is the perpendicular bisector?

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

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Find the area of this one! 12 Hmmmmm….. A circle has 360°… Hmmmmm….. How many degrees would the top angle of each Δ have? Hmmmmm….. Since the Δs are isosceles, what are the measures of the base angles? Hmmmmm….. If the apothem is an angle bisector, then what is the measure of the small top angle? 60° 30° 60° The short side = 6 The apothem = 63 A = 1/2ap A = ½(63)(72) = 2163 (exact) A = (approx.)

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WHEW! Try this… Find the perimeter and area of a Δ with a hypotenuse of 18units. (sketch it) 18 (hint: the smallest angle is across from the smallest side… the largest angle is across from the largest side.) 30° 60° What is the length of the short side? What is the length of the long leg? What is the perimeter? (exact) units What is the area? (exact) 813 sq units or units

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Whiteboard time!!

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Assignment pg 336, 10-21

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