Detailed formula for calculating the area of trapezoids

What is a trapezoid?

According to the textbook Connecting knowledge with life, Math 5, volume 1, lesson 26, a trapezoid in plane geometry is a convex quadrilateral with two opposite sides parallel to each other.

Distinguishing types of trapezoids

Trapezoids can be distinguished by angle or side criteria.

Distinguish by angle	Differentiate by edge
Right trapezoid (trapezoid with 1 side perpendicular to 2 bases)	Regular trapezoid (no equal sides or angles, only 1 pair of parallel opposite sides)
Acute trapezoid (trapezoid with 2 base angles less than 90 degrees)	Isosceles trapezoid (trapezoid has 2 equal angles adjacent to a base, 2 equal sides, 2 equal diagonals, can be inscribed in a circle)
Obtuse trapezoid (trapezoid with 2 opposite angles greater than 90 degrees)

Basic formula for calculating the area of a trapezoid

According to the textbook Connecting knowledge with life, Math 5, volume 1, lesson 26, the area of a trapezoid is equal to the total length of the 2 bases multiplied by the height (same unit of measurement) then divided by 2.

S = ½ [(a+b) xh]

In there:

S: Area of trapezoid

a and b are the lengths of the two bases

h is height

For example: Calculate the area of a trapezoid knowing: The length of the 2 bases are 4cm and 6cm respectively, the height is 3cm

Answer: S = ½ [(4+6) x 3] = 15 cm ²

Do right trapezoids and isosceles trapezoids have formulas for calculating specific area?

No. Even though they are 2 special trapezoids, there is only one formula to calculate a trapezoid.

Tips for calculating the area of a trapezoid

For problems without enough data on the length of the 2 bases and the height, it is impossible to calculate the area of the trapezoid.

Length and area must be converted to the same unit before calculation.