11.2 Area of reg polygons

11.2 Area of reg polygons - 11.2 Areas of Regular Polygons...

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Unformatted text preview: 11.2 Areas of Regular Polygons Polygons p. 669 Thm 11.3 Area of an Equilateral Δ Thm 2 s3 The area of an equilateral Δ is: A = The 4 Where does this come from? s 30o s3 2 s Area of a Δ? A = ½ bh 60o s s 2 1 s 3 A = ( s) 2 2 A= s 2 3 4 Why would you want to know this new area formula? new Ex: Find the area of the equilateral Δ shown. Ex: Instead of having to use Instead 10 cm the 30-60-90 Δ thm to find the height of this Δ, all you the all need is a side length! need 2 s3 A= 4 A= 10 2 3 4 100 3 = 4 = 25 3 ≈ 43.3 cm 2 Definitions (associated with regular Definitions polygons only) polygons Center of a polygon – the center of its circumscribed circle. circumscribed Radius of a polygon – the radius of its circumscribed circle, or the distance from the center to a vertex. from Apothem of a polygon – distance from the center to any side of the polygon. the B F A G E D The center of circle A is: The A The center of pentagon The BCDEF is: BCDEF A C A radius of circle A is: AF A radius of pentagon radius BCDEF is: BCDEF AF An apothem of pentagon An BCDEF is: BCDEF AG Thm 11.4 – Area of a regular polygon Thm The area of a regular polygon is: The A = ½ Pa Pa Area Area Perimeter apothem apothem Ex: A regular octagon has a radius of 4 in. Find its area. of 67.5 o x 4 a 3.7 135o First, we have to find First, the apothem length. the a sin 67.5 = 4 4sin67.5 = a 3.7 = a 1.53 = x Now, the side length. Side length=2(1.53)=3.06 x cos 67.5 = 4 4cos67.5 = x A = ½ Pa = ½ (24.48)(3.7) = 45.288 in2 Last Definition Last Central ∠ of a polygon – an ∠ whose Central vertex is the center & whose sides contain 2 consecutive vertices of the polygon. polygon. ∠ Y is a central ∠ . is Measure of a Measure 360 central ∠ is: n Y Ex: Find m∠ Y. 360/5= 72o Assignment Assignment ...
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