6th Grade Math Textbook, Progress

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 parallelogram
bh


(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 h
4 cm.

A
^1

2

(8 cm) 4 cm

A
16 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

A
100 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

A
59.5 m^2

Think

Rename

70 dm as

meters.

70 dm
7 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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