468 Chapter 13
Area of Trapezoids
13-11
Two congruent trapezoids put together, as in the figure below, form a parallelogram.
Notice that:
- the original trapezoid has 2 bases: the
lower base, b 1 , and the upper base, b 2. - the height, h, is a perpendicular line
segment connecting the 2 parallel bases. - by rotating the original trapezoid 180°,
you can form a parallelogram.
Area of parallelogrambh
(b 1 b 2 )h Substitute (b 1 b 2 ) for b.
The area of the original trapezoid is
one half the area of the parallelogram.
So, the area of a trapezoid^12 (b 1 b 2 ) h.
To find the area of the trapezoid above:
A^1
2
(b 1 b 2 ) h
A^1
2
(5 cm3 cm) 4 cm Substitute b 1 5 cm, b 2 3 cm, and h4 cm.
A^1
2
(8 cm) 4 cm
A16 cm^2
Study these examples.
A^1
2
(b 1 b 2 ) h
A^1
2
(25 in.15 in.) 5 in.
20
A^1
2
^410 ^51
1
A100 in.^2
The formula for the area of a trapezoid:
Area^12 (base 1 base 2 )height
A^12 (b 1 b 2 ) h
A^12 (b 1 b 2 ) h
A^12 (9 m8 m) 7 m
A^12 (17 m) 7 m
A59.5 m^2
Think
Rename
70 dm as
meters.
70 dm7 m
(b 2 ) 3 cm
(b 2 ) 3 cm (b 1 ) 5 cm
(b 1 ) 5 cm
(h) 4 cm
15 in.
25 in.
5 in.
8 m
70 dm
9 m
468 Chapter 13
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