LESSON 7.4 AREAS OF TRAPEZOIDS, RHOMBUSES, AND KITES OBJECTIVE:

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Presentation transcript:

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 and the sum of the bases. b2 b1 h A = ½ h( b1 + b2)

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

lengths of the diagonals. 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 = ½d1d2

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

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

A = ½ h( b1 + b2) A = ½ (12)( 11 + 16) A = (6)( 27) A = 162 ft2 11 ft. C D 11 ft. A = ½ (12)( 11 + 16) A = (6)( 27) A = 162 ft2

A car window is shaped like the trapezoid shown. If the area of the Example #2 A car window is shaped like the trapezoid shown. If the area of the window is 504 in2find the measure of the missing base. Show all steps. 20 in. 18 in.

A = ½ h( b1 + b2) 504 = ½ (18)( 20 + b2) 504 = (9)(20 + b2) 20 in. 18 in. 504 = ½ (18)( 20 + b2) 504 = (9)(20 + b2) 56 = 20 + b2 36 in. = b2

Find the area of kite WXYZ. Example #3 Find the area of kite WXYZ. d2 = 1 + 4 = 5 d1 = 3 + 3 = 6 W X Y Z 3 cm 4 cm 1 cm

W X Y Z 3 cm 4 cm 1 cm A = ½ d1d2 A = ½(6)(5) A = 15 cm2

Example #4 If the area of rhombus RSTU is 120 ft2, then find the measure of the missing diagonal. 24 ft. U R S T

A = ½ d1d2 24 ft. U R S T 120 = ½(24)d2 120 = 12d2 10 ft = d2

ASSIGNMENT: Worksheet 7.4 Min. 3 lines per problem plus units