Ch 10.5 Find the area of the figure. Round to the nearest tenth if necessary. 5 (10 + 18) = 70 2 Trapezoid LMNO has an area of 55 square units. Find the height. 55 = h (8 + 14)  h = 5 2 Find the height of a trapezoid that has an area of 64 square inches, and bases of 8 and 12 inches. 64 = h (8 + 12)  h = 6.4 cm 2

Ch 10.5 Areas of Regular Polygons Learning Target: I will be able to find the areas of regular polygons. Standard 10.0 Students compute areas of polygons.

Ch 10.5 Area of a Regular Polygon FURNITURE The top of the table shown is a regular hexagon with a side length of 3 feet and an apothem of 1.7 feet. What is the area of the tabletop to the nearest tenth? Step 1 Since the polygon has 6 sides, the polygon can be divided into 6 congruent isosceles triangles, each with a base of 3 ft and a height of 1.7 ft.

Ch 10.5 Step 2 Find the area of one triangle. Area of a triangle Area of a Regular Polygon Step 2 Find the area of one triangle. Area of a triangle b = 3 and h = 1.7 Simplify. = 2.55 ft2 Step 3 Multiply the area of one triangle by the total number of triangles. Since there are 6 triangles, the area of the table is 2.55 ● 6 or 15.3 ft2.

Ch 10.5 UMBRELLA The top of an umbrella shown is a regular hexagon with a side length of 2 feet and an apothem of 1.5 feet. What is the area of the entire umbrella to the nearest tenth? A. 6 ft2 B. 7 ft2 C. 8 ft2 D. 9 ft2 Example 2

Ch 10.5 center of a regular polygon a point in the interior that is equidistant from all the vertices. apothem a segment drawn from the center that is perpendicular to a side of the regular polygon. Note: In any regular polygon, all apothems are congruent. Vocabulary

Ch 10.5 Identify Center and Apothem in Regular Polygons In the figure, pentagon PQRST is inscribed in Identify the center and apothem of the polygon. center: point X apothem: XN

Ch 10.5 Theorem 10-5 Concept

Ch 10.5 Use the Formula for the Area of a Regular Polygon A. Find the area of the regular hexagon with a side length of 5 meters and an apothem of 2.5√3 meters. 2.5√3 m Area of a regular polygon ≈ 65.0 m2 Use a calculator.

Ch 10.5 A. Find the area of the regular hexagon with sides of 7.5 m and apothem of 6.5 m. Round to the nearest tenth. A. 73.1 m2 B. 96.5 m2 C. 126.8 m2 D. 146.3 m2 Example 3

Ch 10.5 Use the Formula for the Area of a Regular Polygon B. Find the area of the regular pentagon with a side length of 10.58 cm and an apothem of 7.28 cm. Round to the nearest tenth. Area of a regular polygon Use a calculator. Example 3B

Ch 10.5 B. Find the area of the regular pentagon with a side length of 7 m and an apothem of 6.5 m. Round to the nearest tenth. A. 113.8 m2 B. 124.5 m2 C. 138.9 m2 D. 143.1 m2 Example 3

Ch 10.5 Find the area of the shaded figure. Find the Area of a Composite Figure by Subtracting Find the area of the shaded figure. To find the area of the figure, subtract the area of the smaller rectangle from the area of the larger rectangle. The length of the larger rectangle is 25 + 100 + 25 or 150 feet. The width of the larger rectangle is 25 + 20 + 25 or 70 feet.

Ch 10.5 area of shaded figure = area of larger rectangle Find the Area of a Composite Figure by Subtracting area of shaded figure = area of larger rectangle – area of smaller rectangle Area formulas Substitution Simplify. Simplify. Example 5

Ch 10.5 INTERIOR DESIGN Cara wants to wallpaper one wall of her family room. She has a fireplace in the center of the wall. Find the area of the wall around the fireplace. A. 168 ft2 B. 156 ft2 C. 204 ft2 D. 180 ft2 Example 5