Technical Mathematics, Sixth Edition

6.3. Quadrilaterals

A quadrilateral is a polygon having four sides. They are the familiar figures shown in Fig. 6-55. The formula for the area of each interior is given right on the figures (b)–(f).

For the parallelogram, opposite sides are parallel and equal. Opposite angles are equal, and each diagonal cuts the other diagonal into two equal parts (they bisect each other).

The rhombus is also a parallelogram, so the previous facts apply to it as well. In addition, its diagonals bisect each other at right angles and bisect the angles of the rhombus.

The trapezoid has two parallel sides, which are called the bases, and the altitude is the distance between the bases.

Example 12: The area of a square of side 5.84 m is Area = (5.84)2 = 34.1 m2 rectangle measuring 3.85 ft by 7.88 ft is Area = (3.85)(7.88) = 30.3 ft2 parallelogram having a height of 6.22 cm and a base of 9.36 cm is Area = (6.22)(9.36) = 58.2 cm2 rhombus of altitude 2.81 m and a base of 4.25 m is Area = (2.81)(4.25) = 11.9 m2 trapezoid with bases 17.4 in. and 22.6 in. and altitude 12.9 in. is

Figure 6.55. Quadrilaterals.

Example 13: An Application. A solar collector array consists of six rectangular panels, each 45.3 in. × 92.5 in., Fig. 6-56. The collecting area of each panel is reduced by a connection box measuring 4.70 ...