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Warm Up

Warm Up. Ms. Kenny’s class is making felt banners for tonight’s basketball game. Each banner will be shaped like a triangle with a base of 2/3 foot long and a height of 1 foot. How much felt will we need to make 30 banners?. Royals. 1 ft. 2/3 ft.

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Warm Up

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  1. Warm Up Ms. Kenny’s class is making felt banners for tonight’s basketball game. Each banner will be shaped like a triangle with a base of 2/3 foot long and a height of 1 foot. How much felt will we need to make 30 banners? Royals 1 ft 2/3 ft

  2. Measurement (continued)Perimeter and Area of Regular Polygons Objectives: students will understand what it means to have a regular polygon and calculate perimeter and area. Warm Up Check Homework Take notes Perimeter and area of regular polygons Carnegie

  3. Regular Polygons • A polygon is Regular if the sides are all the same length. • We already worked with a regular quadrilateral; the square. • Usually indicated by marks;

  4. Perimeter of Regular Polygons • To find the perimeter of a regular polygon, add up the sides – OR – • Multiply the length by the number of sides the polygon has. • P = ns; n is the number of sides of the polygon. 3.5 yd 7 cm 13 ft

  5. Area of Regular Polygons • Regular Polygons also have a center point. A segment drawn from this center point that is perpendicular to a side is called the apothem. apothem

  6. Apothem Vs. Altitude (Height) Same • Both form right angles with the base of their figures • Different • Apothem starts at the center of the polygon. Altitude goes from one side of the polygon to the other.

  7. Area of a Regular Polygon • First, notice that you can split a regular • polygon into triangles • The number of sides the polygon • has is the number of triangles it can • be split into. In this case, we can split a hexagon into 6 triangles. • We know the area of a triangle is A = ½ bh **remember, we have 6 of these triangles • Ahexagon = 6 (1/2 bh) *This is not the formula yet!!!

  8. Area of a Regular Polygon • We also know that the perimeter of this shape is P = 6s • We can re-write this as P = 6b since the base of the triangle is the whole side of the hexagon. • We can also re-write our triangle formula to A = ½ ba; a is the apothem of the polygon. • Now we can change our formula around; Ahexagon = 6 (1/2 bh) is now A = 1/2 Pa

  9. Examples Remember: A = ½ Pa 3 m 2.2 m • An regular octagon has an area of 76.8 square centimeters. If its side measures 4 centimeters , how long is the apothem?

  10. Examples 7 ft • A hexagon with an apothem of 20 meters has an area of 1386 square meters. How long is each side? 6 ft

  11. Examples • The Pentagon building in Washington, D.C. is named for its shape. If the perimeter of the building is 2300 feet, how long is each side? • If the length from the center of the building to one wall is 398 feet, what is the area of the building?

  12. Examples • A castle in Italy, the Castel del Monte, is shaped like a regular octagon. There is a courtyard inside that is the same shape. Each wall of the castle is 25 feet long, and the apothem is 30.2 feet. Each wall of the courtyard is 12 feet and its apothem is 14.5 feet. What is the total area of the castle? What is the total area of the courtyard? 12 ft 14.5 ft 30.2 ft 25 ft

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