([DPSOH
A trapezoid has bases of length a and b and height h,
as shown in )LJXUH. Find a formula for its area.
6ROXWLRQ
Draw a diagonal, as shown in )LJXUH.
We see that area 11 122 2ah bh a b h.
Comment: A triangle can be regarded as a trapezoid
with base a of length 0.
([DPSOH
A regular hexagon has area 100 cm^2. What is its side length?
6ROXWLRQ
Call the side length of the regular hexagon s, as shown
in )LJXUH.
The interior angle of a regular hexagon is ^3606 D
7KXVWKHVKDGHGWULDQJOHVKRZQKDVLQWHULRUDQJOHVDQGLV
an equilateral triangle.
The Pythagorean theorem gives the height of the triangle as
(^22233).
sss §· ̈ ̧©¹ 242 s^
Thus, the area of the hexagon is 6.u^1 22 2ss^333 s^2
6HWWLQJWKLVHTXDOWRJLYHVs^2 33210033200 , so s 33200 cm.
6WXG\7LS
x 2QO\NHHSWKHIRUPXODVIRUWKHDUHDRIDUHFWDQJOHDQGWKHDUHDRIDWULDQJOHLQPLQGͼ,QIDFWWKH\DUH
SUREDEO\DOUHDG\WKHUHIURPHDUO\VFKRROGD\Vͽ$OORWKHUIRUPXODVUHDGLO\IROORZIURPWKHVHLI\RX
keep your wits about you.
a
h
b
Figure 21.3
a
h
b
Figure 21.4
S
S
S
S S
60°S 2 S 2
Figure 21.5