* * * * * * * * * E x a m p l e * * * * * * * * *
A trapezoid has bases that are 30 and 55 centimeters in length and the nonparallel sides (or legs) are 15 and 20 centimeters.
What is the area of the trapezoid?
Going by the diagram, we shall label the 4 sides as:
a = 55 b = 15 c = 30 d = 20
Before we can use the area formula, we first have to determine the height of the trapezoid.
(height)^{2} = (a+bc+d) • (a+b+c+d) • (abc+d) • (a+bcd) ÷ (4 • (a c)^{2})
(height)^{2} = (55+1530+20) • (55+15+30+20) • (551530+20) • (55+153020) ÷ (4 • (55 30)^{2})
(height)^{2} = (60) • (10) • (30) • (20) ÷ (4 • (25)^{2})
(height)^{2} = 360,000 ÷ 2,500
(height)^{2} = 144
height = 12 cm
Now to use the area formula:
trapezoid area = ((sum of the bases) ÷ 2) • height
trapezoid area = ((55 + 30) ÷ 2) • 12
trapezoid area = 510 cm²
To see how to calculate trapezoid area without using formulas, click here.
* * * * * * * * * Trapezoids * * * * * * * * *
ALL TRAPEZOIDS have the following
properties: 1) ONE pair of opposite sides are parallel.
(BC and AD)
2) The sum of the angles attached to the same leg = 180°
∠ 'A' plus ∠ 'B' = 180°
∠ 'C' plus ∠ 'D' = 180°
4 special cases of trapezoids are worth mentioning.
The isosceles trapezoid has
both legs of equal length. AB = CD
Both diagonals are equal. AC = BD
Lower base angles are equal. ∠ A = ∠ D
Upper base angles are equal. ∠ B = ∠ C
Angles attached to the same leg are supplementary. ∠ A + ∠ B = 180° ∠ C + ∠ D = 180°
Opposite angles are supplementary. ∠ A + ∠ C = 180° ∠ B + ∠ D = 180°
The right trapezoid has
two right angles.
The acute trapezoid has two acute angles located on each side of the long base.
The obtuse trapezoid has two obtuse opposite angles (A & C) and two acute opposite angles(B & D).
or
it has one acute angle and one obtuse angle on each base.
* * * * * * * * * Formulas for Calculating Trapezoid Diagonals * * * * * * * * *
