![]() Quick Check 10-3įind the area of a regular polygon with twenty 12-in. ![]() Areas of Regular Polygons Lesson 10-3 Additional Examples Finding Angle Measures A portion of a regular hexagon has an apothem and radii drawn. 1 2 m 3 = 180 – (90 + 30) = 60 The sum of the measures of the angles of a triangle is 180. m 2 = m 1The apothem bisects the vertex angle of the isosceles triangle formed by the radii. 10-3Īreas of Regular Polygons Lesson 10-3 Notes 10-3ģ60 6 m 1 = 60 Divide 360 by the number of sides. 10-3Īrea of each triangle: total area of the polygon: Areas of Regular Polygons Lesson 10-3 Notes To find the area of a regular n-gon with side length s and apothem a, divide it into n congruent isosceles triangles. Each central angle measure of a regular n-gon is 10-3Īreas of Regular Polygons Lesson 10-3 Notes Regular pentagon DEFGH has a center C, apothem BC, and central angle DCE. ![]() A central angle of a regular polygonhas its vertex at the center, and its sides pass through consecutive vertices. The apothemis the distance from the center to a side. The radius of a regular polygon is the distance from the center to a vertex. 10 3 20 3 20 3 1 2 1 2 10-3Īreas of Regular Polygons Lesson 10-3 Notes The center of a regular polygonis equidistant from the vertices. Since each side has length 2 3 cm, the perimeter is (8)(2 3) = 16 3 cm. A regular octagon has eight sides of the same length. The perimeter of a polygon is the sum of the lengths of its sides. Since each side has length 4 in., the perimeter is = (6)(4) = 24 in. A regular hexagon has six sides of the same length. Thus the base of the equilateral triangle is m. Since the long leg of the 30°-60°-90° triangle is 10m the short leg is m and the hypotenuse is m. The altitude divides the triangle into two 30°-60°-90° triangles. The triangle is equilateral and equiangular, so each of its angles is 60°. 1 2 1 2 10 2 Areas of Regular Polygons Lesson 10-3 Check Skills You’ll Need 10-3Ģ0 3 100 3 100 3 3 Areas of Regular Polygons Lesson 10-3 Check Skills You’ll Need Solutions (continued) 3. The diagonal is 10 cm and divides the square into two 45°-45°-90° triangles. The base is 10 cm and the height is 5 3 cm. Since the short leg of the 30°-60°-90° triangle is 5cm, the long leg, which is the altitude of the equilateral triangle, is 5 3 cm. ![]() an octagon with sides of 2 3 cm Find the perimeter of the regular polygon. If your answer involves a radical, leave it in simplest radical form. rhombus MNOP 99 cm2 26 square units 840 mm2 10-3Īreas of Regular Polygons Lesson 10-3 Check Skills You’ll Need (For help, go to Lesson 8-2.) Find the area of each regular polygon. kite with diagonals 20 m and 10 2 m long 5. ![]() Leave your answers in simplest radical form. Find the area of each figure in Exercises 3–5. Find the area of a trapezoid in a coordinate plane with vertices at (1, 1), (1, 6), (5, 9), and (5, 1). Find the area of a trapezoid with bases 3 cm and 19 cm and height 9 cm. 94.5 3 in.2 100 2 m2 Areas of Trapezoids, Rhombuses, and Kites Lesson 10-2 Lesson Quiz 1. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |