How to find the area of a trapezoid and the area of a rhombus or a kite. Chapter 10.2GeometryStandard/Goal 2.2

1. Check and discuss the assignment from yesterday. 2. Read, write, and discuss how to find the area of a trapezoid. 3. Read, write, and discuss how to find the area of a rhombus or a kite. 4. Work on assignment.

Height of a trapezoid is the perpendicular distance h between the bases.

The area of a trapezoid is half the product of the height and the sum of the bases. h

The area of a kite is half the product of the length of its diagonals.

The area of a rhombus is equal to half the product of the lengths of the diagonals.

A car window is shaped like the trapezoid shown. Find the area of the window. A = 504Simplify. The area of the car window is 504 in. 2 A = h ( b 1 + b 2 )Area of a trapezoid 1212 A = (18)( )Substitute 18 for h, 20 for b 1, and 36 for b Lesson 10-2

Find the area of trapezoid ABCD. Draw an altitude from vertex B to DC that divides trapezoid ABCD into a rectangle and a right triangle. Because opposite sides of rectangle ABXD are congruent, DX = 11 ft and XC = 16 ft – 11 ft = 5 ft. Lesson 10-2

(continued) By the Pythagorean Theorem, BX 2 + XC 2 = BC 2, so BX 2 = 13 2 – 5 2 = 144. Taking the square root, BX = 12 ft. You may remember that 5, 12, 13 is a Pythagorean triple. A = 162Simplify. The area of trapezoid ABCD is 162 ft 2. A = h ( b 1 + b 2 )Use the trapezoid area formula A = (12)( )Substitute 12 for h, 11 for b 1, and 16 for b Lesson 10-2

Find the lengths of the diagonals of kite XYZW. XZ = d 1 = = 6 and YW = d 2 = = 5 A = 15Simplify. The area of kite XYZW is 15 cm 2. A = d 1 d 2 Use the formula for the area of a kite A = (6)(5)Substitute 6 for d 1 and 5 for d Find the area of kite XYZW. Lesson 10-2

Find the area of rhombus RSTU. Lesson 10-2 To find the area, you need to know the lengths of both diagonals. Draw diagonal SU, and label the intersection of the diagonals point X.

The diagonals of a rhombus bisect each other, so TX = 12 ft. You can use the Pythagorean triple 5, 12, 13 or the Pythagorean Theorem to conclude that SX = 5 ft. SU = 10 ft because the diagonals of a rhombus bisect each other. A = 120Simplify. The area of rhombus RSTU is 120 ft 2. A = d 1 d 2 Area of a rhombus 1212 A = (24)(10)Substitute 24 for d 1 and 10 for d Lesson 10-2 (continued) SXT is a right triangle because the diagonals of a rhombus are perpendicular.

Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.