7.4: Areas of Trapezoids, Rhombuses, and Kites

Objective:1. To find the areas of

trapezoids, rhombuses, and kites

ExampleFind the area of the parallelogram

Bases and Heights

The parallel sides of a trapezoid are the basesbases. The altitudealtitude is a segment connecting the bases that is perpendicular to both. The length of the altitude (the distance between the bases) is the heightheight.

b1

b2

Height (h)

How to find area

Area of a Trapezoid Theorem

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

2

)()(

2

1 2121

bbhbbhA

Example 2Find the area of the trapezoid.

22 cm

13 cm 10 cm

18 cm5 cm

Investigation

The following investigation will demonstrate how to compute the area of a kite.

d2

d1

Area of a kite

Area of a Kite Theorem

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

d2

d1

d2

d1

22

1 2121

ddddA

Example Find the area of the kite to the nearest whole

square unit.

Area of a Rhombus

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

Area of a Rhombus

Area of a Rhombus Theorem

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

22

1 2121

ddddA

ExampleFind the area of the rhombus.

Example Find the area of each polygon.

How you could find the area of the regular hexagon shown.

Example Find the area of each regular polygon.