LESSON 7 4 AREAS OF TRAPEZOIDS RHOMBUSES AND

LESSON 7. 4 AREAS OF TRAPEZOIDS, RHOMBUSES, AND KITES OBJECTIVE: To find the areas of trapezoid, rhombuses, and kites

Theorem 7 -10 Area of a Trapezoid The area of a trapezoid is one-half the product of the height b and the sum of the bases. 1 A = ½ h( b 1 + b 2) h b 2

The height (h) of a trapezoid is the distance between the two bases.

Theorem 7 -1: Area of a Rhombus or a kite The area of a rhombus or kite is half the product of the lengths of the diagonals. A = ½d 1 d 2

Reminder: A rhombus is also a parallelogram. We will use A = bh most of the time.

Example #1 Find the area of trapezoid ABCD. (Show formula, substitution, & simplify. ) 11 ft. B 12 ft. A D 5 ft. C

A = (6)( 27) A = 162 ft 2 A 11 ft. B 12 ft. A = ½ h( b 1 + b 2) A = ½ (12)( 11 + 16) D 5 ft. C

Example #2 A car window is shaped like the trapezoid shown. If the area of the window is 504 in 2 find the measure of the missing base. Show all steps. 20 in. 18 in.

A = ½ h( b 1 + b 2) 504 = ½ (18)( 20 + b 2) 504 = (9)(20 + b 2) 56 = 20 + b 2 36 in. = b 2 20 in. 18 in.

Example #3 Find the area of kite WXYZ. d 2 = 1 + 4 = 5 d 1 = 3 + 3 = 6 Y X 1 cm 3 cm Z 4 cm W

Y A = ½ d 1 d 2 X A = ½(6)(5) A = 15 cm 1 cm 3 cm Z 4 cm 2 W

Example #4 If the area of rhombus RSTU is 120 ft 2, then find the measure of the missing diagonal. S R 24 ft. U T

A = ½ d 1 d 2 24 ft. 120 = ½(24)d 2 120 = 12 d 2 10 ft = d 2 S R U T

ASSIGNMENT: Worksheet 7. 4 Min. 3 lines per problem plus units