5-9 Honors Geometry Warm-up Find the area of the shaded region if AB= BC= CD. A B C D.

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Presentation transcript:

5-9 Honors Geometry Warm-up Find the area of the shaded region if AB= BC= CD. A B C D

A bakery sells single-layer mini-cakes that are 3 inches in diameter for $4 each. They also have a 9-inch cake for $15. Which cake is more economical?

HW: p.613 #8-22even, p. 615 # in cm in units units units in units units units units units 2

These formulas work for any regular polygon (even a polygon that isn’t inscribed.) In the below formulas, A = the area of the polygon a = the length of the apothem q = the number of sides of the polygon p = the length of half a side of the polygon (or, Perimeter ÷ 2q) r = the distance from the center of the polygon to any vertex (in inscribed polygons, this is the radius of the circle) Spending too much time on those pesky area-of-a-polygon problems? Well, it’s your lucky day. a r p So the basic formula is: A = a × p × q Use this if you know the area but have to find one of the other measures. Use this formula if you know the perimeter or side length of the polygon: A = p² × q tan(180 tan(180 ÷ q) Use this formula if you know the length of the apothem of the polygon: A = a² × q × tan(180 A = a² × q × tan(180 ÷ q) Use this formula if you know the length of the radius: A = r² × q × sin(180 × cos(180 A = r² × q × sin(180 ÷ q) × cos(180 ÷ q)