What is the Concept of the Trapezoid? How to use the Trapezoid Area Formula?

In this article, you will learn what trapezoidal area is and how to calculate it. Also learn the formula of trapezoidal area.

What is a Trapezoid Area?

The trapezoid area refers to the amount of space covered by the sides of a trapezoid shape. A trapezoid is a four legs shape having a pair of parallel sides. It is a quadrilateral that is a plane and closed shape. The area covered by a trapezoid can be calculated by using formula or by splitting it into smaller polygons like triangles and rectangles and then finding their areas, and adding them to get the area of a trapezoid.

Trapezoid Area Formula

If A is the area of trapezoid, h be the height, a and b are parallel sides then the formula for area of a trapezoid is:

We can calculate the area of trapezoid by adding the parallel bases of trapezoid together and multiplying it with h and then dividing by 2.

For example, in a given trapezoid, the area can be calculated as:

The length of bases of given trapezoid are:

b₁ = 8cm and b ₁ = 6cm

And the height or distance between the bases is:

h = 10cm

The trapezoid area will be:

$$ A \;=\; \frac{1}{2}(b_1 + b_2)h $$ $$ A \;=\; \frac{1}{2}(8 + 6) \times 10 $$ $$ A \;=\; \frac{1}{2}(140) $$ $$ A \;=\; 70cm $$

How to calculate the Area of a Trapezoid?

The area of trapezoid can be calculated by using the bases and height of trapezoid in the area formula, that is:

$$ A \;=\; \frac{1}{2}(a+b)h $$

See the following examples to understand how to calculate the area of a trapezoid.

Volume of Trapezoid Formula

The volume of a trapezoid is the total space occupied by it in three dimensions. It can be calculated by multiplying the area and height of the trapezoid. The formula to calculate volume of a trapezoid is:

V = Area × height
or
V = A × h

So this is the volume of trapezoid formula to calculate the volume of trapezoid. Let's understand how to use this formula to understand the concepts of volume of a trapezoid.

For example to calculate volume of the above example 2, where,

A=62.5cm and h=5cm

Then, the volume will be,

V=62.55

V=312.5cm²

Related Formula's

1. Area of Sector Formula
$$ A \;=\; \frac{θ}{360} \pi r^2 $$

Where,
θ = angle in degree

2. Area of Square Formula
$$ A \;=\; S^2 $$

Where,
S = any side of square

3. Area of Pentagon Formula
$$ A \;=\; \frac{1}{2} P \times A $$

Where,
P = Perimeter
A = Apothem

4. Circumference Formula
$$ C \;=\; 2 \pi r $$

Where,
r = radius of circle

Frequently Asked Questions (FAQ's)

What is the Formula for the Area of Trapezoid?

The Formula for Area of a Trapezoid is:

$$ A \;=\; \frac{1}{2}(a+b)h $$

Where, a and b are the length of parallel sides and h be the height of trapezoid.

What are the Bases and Legs of a Trapezoid?

The bases of a trapezoid are its parallel sides and the legs are non-parallel sides.