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7.4: Areas of Trapezoids, Rhombuses, and Kites. Objective: To find the areas of trapezoids, rhombuses, and kites. Example. Find the area of the parallelogram. Bases and Heights. - PowerPoint PPT Presentation
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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.