7-4 Area of Trapezoids, Rhombuses, and Kites

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Areas of Trapezoids, Rhombuses, and Kites

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7-4 Area of Trapezoids, Rhombuses, and Kites 3/10/17 7-4 Area of Trapezoids, Rhombuses, and Kites Objective: To find the area of a trapezoid, rhombus, or kite. HEIGHT OF A TRAPEZOID: the perpendicular distance h between the bases THEOREM 7-10 AREA OF A TRAPEZOID The area of a trapezoid is half the product of the height and the sum of the bases. A = ½ h (b1 + b2) b1 h b2

THEOREM 7-11 AREA OF A RHOMBUS OR A KITE Ex: S 5m R A = ½ h (b1 + b2) h A = ½ (2 3)(7 + 5) 60o A = 12 3 m2 P Q 7 m THEOREM 7-11 AREA OF A RHOMBUS OR A KITE The area of a rhombus or a kite is half the product of the lengths of its diagonals. A = ½ d1d2 = 2 3 2 d1 d2

Ex: Find the area of kite KLMN. KM = 7 and LN = 6 THEOREM 7-11 AREA OF A KITE OR RHOMBUS The area of a kite or a rhombus is half the product of the diagonals. A = ½d1d2 Ex: Find the area of kite KLMN. KM = 7 and LN = 6 A = ½ d1d2 Area of kite L A = ½ (7)(6) Substitute 3m A = 21 m2 Simplify K 2m 5m M 3m N Find the area of a kite with diagonals that are 12 in and 9 in long. A = ½ (12)(9) = 54 in2

Ex: Find the area of rhombus ABCD. 9 15 E 12 Ex: Find the area of rhombus ABCD. BE = 9 using the Pythagorean triple. Since the diagonals of a rhombus bisect each other, AC = 24 and BD = 18. A = ½ d1d2 Area of rhombus = ½ (24)(18) Substitute = 216 m2 Simplify A D

Find the area of Rhombus RSTV R S ST = 13, RT = 24 V T Find the area of Kite WXYZ Y X 1 cm 4 cm Z 3 cm W 5 12 A = ½ (24)(10) = 120 13 5 12 3 A = ½ (6)(5) = 15 cm2

Find the area of a trapezoid with bases 3 m and 19 m and height 9 m. A = ½(9)(3 + 19) = 9(11) = 99 m2 Find the area of a trapezoid with bases 3 m and 19 m and height 9 m. 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. Leave it in simplest radical form. Trapezoid ABCD C 10 in D 14 in B Kite with diagonals 20 m and 10 2 m long Rhombus MNOP N 29 mm M 42 mm O P A = ½(4)(5 + 8) = 26 A = ½(7 3)(10 + 17) = ½ 189 3 7 3 F 60° A 7 A = ½(20)(10 2) = 100 2 20 A = ½(40)(42) = 840 mm2 21

Assignment: Page 376 #2 – 20 even, 27 – 35 odd