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7.5 Areas of Regular Polygons

7.5 Areas of Regular Polygons. Chapter 7 Area. 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. Fats, oils, sweets Fruit Bread, cereal, rice,

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7.5 Areas of Regular Polygons

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  1. 7.5 Areas of Regular Polygons Chapter 7 Area

  2. 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. • Fats, oils, sweets • Fruit • Bread, cereal, rice, and pasta 5.2 cm Fats, Oils, & Sweets 15.6 cm2 3 cm 3 cm Meat, Poultry, Fish, Eggs, & Nuts 35cm2 Milk, Yogurt, &Cheese 6cm 5cm Vegetables Fruit 105 cm2 10cm 8cm 5cm Bread, Cereal, Rice, & Pasta 24cm

  3. 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? A = ½ h(b1 + b2) A = ½ (10)(50+30) A = 400 yd2 50 yd 50 yd 30 yd 30 yd Area = 1200 yd2 30 yd Cost = (1200)($1.59) Cost = $1908 50 yd

  4. 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)

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

  6. Find the area of these regular polygons. Find the area of the shaded region. 7.8 in 8.0 ft 5.5 ft 9 in Area of Pentagon – Area of Triangle A = ½ (7.8)(54) Pentagon: A = ½ (5.5)(40) A = 110 A = 210.6 in2 Triangle: A = ½ (5.5)(8) A = 22 Area of Shaded Region: 110 – 22 88 ft2

  7. 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 Step 3: Use the formula to find the area A = ½ (0.8)(5.4) A = 2.16 in2 0.8 in 0.9 in

  8. Find the area of the region above the red line in the regular polygon. Area of the octagon – Area of the trapezoid Area of the octagon: A = ½ (2.4)(16) 2.4 m A = 19.2 m2 4.8 m Area of the trapezoid: 1.4 m A = ½ (1.4)(2.0 + 4.8) A = 4.76 m2 2.0 m Area of the region above the red line: 19.2 – 4.76 14.44 m2

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