Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 14: Quadrilaterals 191

The height of the parallelogram is half the height of the trapezoid. The base of the parallelogram
is the sum of the length of the long and the short base of the trapezoid. So the area of a trapezoid
is equal to half the height multiplied by the sum of the bases.

WORDLY WISDOM

Some people remember this formula as the average of the bases times the height, or

the length of the median times the height.

Try using that formula to figure out the height of a trapezoid with an area of 40 square
centimeters and bases 3 cm and 5 cm. Plug those numbers into the formula.

The height of the trapezoid is 10 centimeters.

P P P

DCD A

C

Q

A B

A^1 hb b

2 12



A^1 hb b

2 12



40 1

2

35

40 1

2

8

40 4

10









h

h

h

h

CHECK POINT

16. Find the perimeter and area of a square with a side of 17 cm.


17. Find the perimeter and area of a rectangle 18 inches long and 9 inches wide.


18. Find the area and perimeter of parallelogram ABCD if AB = CD = 7 inches, AC
    = BD = 21 inches, and the height from B perpendicular to AC is 3 inches.


19. Find the perimeter and area of a rhombus with sides 5 inches long if the diago-
    nals measure 6 inches and 8 inches.


20. The area of a parallelogram with a height of 48 cm is 3,600 square centimeters,
    and its perimeter is 250 cm. Find the lengths of the sides of the parallelogram.