Trapezoid

A trapezoid is a quadrilateral with one pair of parallel sides. So, this four-sided polygon is a plane figure and a closed shape. It has four line segments and four interior angles. The parallel sides are the trapezoid's two bases; the other two sides are its legs.

The perimeter of a trapezoid:

Perimeter = Sum of all the sides

Perimeter = AB + BC + CD + DA

Area of a trapezoid

Area = h x (b₁ + b₂ )/2

where

b₁ , b₂ are the lengths of each base

h is the altitude (height)

Example:

Find the area of the trapezoid if the two bases are 5 cm and 7 cm respectively. Also, the height is given as 8 cm.

Solution:

Area = 8 x (5+ 7)/2

= 8 x (12)/2

= 8 x 6

= 48 cm2

To find the height and base of the trapezoid that is used in the area of a trapezoid formula, we need to use the following formulas.

Height (altitude) = 2a/(b₁ + b ₂ )

Where a = area and b₁ , b₂ are the 2 bases.

Base length = (2a/h) – b

Where a = area and b = base, and h is the height (altitude).

Area = mh

Where m = median and h = height (altitude).