Trapezoid formula
In geometry, a trapezium is a quadrilateral with one pair of parallel sides (called bases) and one pair of non-parallel sides (called legs). The area of a trapezium is the number of unit squares that can fit inside it. It is often measured in square units like cm2, m2, and so forth. In this post, we will look at the area of a trapezium formula and several instances.
Area of Trapezoid Formula
The area is defined as the area or region that the trapezium occupies. It is equal to half of the total of its bases multiplied by their distance. The area of a trapezium is given as:
Area of a Trapezoid = (1/2) × h × (a + b)
where,
- a = Shorter base
- b = Longer base
- h = Height or distance between the two bases
Examples on Area of Trapezoid
Example 1: Calculate the area of a trapezoid whose parallel sides are 22 cm and 12 cm, respectively, and whose height is 6 cm.
Solution: The bases are given as, a = 22 cm; b = 12 cm; the height is h = 6 cm.
The area of the trapezoid = A = ½ (a + b) h
A = ½ (22 + 12) × (6) = (34) × (3) = 102 cm2.
Example 2: Calculate the height of the trapezoid, if the sum of the parallel sides is 30 m and the area is 60 m2.
Solution:
Given: a+b = 30 m
Area, A = 60 m2.
To find: h
We know that the formula for area of trapezoid, A = (½) [(a+b)h] square units
Substituting the values in the formula, we get
60 = (½)[30h]
60/30 = (½)h
2 = h/2
h = 4.
Therefore, the height of the trapezoid is 4 m.