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7.5 Areas of Regular Polygons Chapter 7 Area

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Bellwork The Food Guide Pyramid outlines foods you should eat for a healthy diet. One face of the pyramid is a triangle displaying the food groups. Find the area used for each food group below. a. Fats, oils, sweets b. Fruit c. Bread, cereal, rice, and pasta Fats, Oils, & Sweets Meat, Poultry, Fish, Eggs, & Nuts Milk, Yogurt, &Cheese VegetablesFruit Bread, Cereal, Rice, & Pasta 5.2 cm 3 cm 5cm 6cm 10cm8cm 5cm 24cm 15.6 cm 2 35cm 2 105 cm 2

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Bellwork It costs $1.59 per square yard to seal an asphalt parking lot area. How much will it cost to seal the parking lot surface below if all of the sections are 10 yards deep? 50 yd 30 yd A = ½ h(b 1 + b 2 ) A = ½ (10)(50+30) A = 400 yd 2 Area = 1200 yd 2 Cost = (1200)($1.59) Cost = $1908

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Areas of Regular Polygons Center: a point in the interior that is equidistant from all vertices Apothem: a segment drawn from the center that is perpendicular to a side of the regular polygon; (in a regular polygon all apothems are congruent)

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Area of a Regular Polygon A = ½ aP a = apothem P = perimeter of the polygon a P

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Find the area of these regular polygons. 7.8 in 9 in 5.5 ft 8.0 ft Find the area of the shaded region. A = ½ (7.8)(54) A = 210.6 in 2 Area of Pentagon – Area of Triangle Pentagon: A = ½ (5.5)(40) A = 110 Triangle: A = ½ (5.5)(8) A = 22 Area of Shaded Region: 110 – 22 88 ft 2

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Each of the tiles in a game is a regular hexagon. Find the area of one of the tiles if the sides are each 0.9 inch long and each apothem is 0.8 inch long. Step 1: Draw a picture Step 2: Label the picture 0.9 in 0.8 in Step 3: Use the formula to find the area A = ½ (0.8)(5.4) A = 2.16 in 2

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Find the area of the region above the red line in the regular polygon. 1.4 m 2.4 m 4.8 m 2.0 m Area of the octagon – Area of the trapezoid Area of the octagon: A = ½ (2.4)(16) A = 19.2 m 2 Area of the trapezoid: A = ½ (1.4)(2.0 + 4.8) A = 4.76 m 2 Area of the region above the red line: 19.2 – 4.76 14.44 m 2

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The Apothem The apothem (a) is the segment drawn from the center of the polygon to the midpoint of the side (and perpendicular to the side)

The Apothem The apothem (a) is the segment drawn from the center of the polygon to the midpoint of the side (and perpendicular to the side)

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