How do we find the area of irregular shapes if none of its sides are known?

To find the area of an irregular shape, divide the shape into unit squares. Count the number of squares that cover the shape completely. If the shape does not occupy complete unit squares, estimate the number of unit squares that will fill it.

Why is area a 2-dimensional quantity?

The area of any shape is the space occupied by it on a plane surface. Therefore, area is a two-dimensional quantity as well.

What is the area of a parallelogram?

Area of a parallelogram = Base × Height

What is the difference between area and volume?

The space inside the boundary of a two-dimensional shape is known as area, whereas the space occupied by a 3-dimensional object is its volume.

What is Area of Shape? - Definition, Facts and Examples

Area of Shapes

Geometric shapes are the figures with a set of points connected by lines resulting in a closed figure.

For example, triangle, square, rectangle and quadrilateral are shapes with 3 and 4 points connected by lines. Shapes with bounded curves don’t have sides but have the circumference.

Mirrors of different shapes with sides and curves.

Area

The area of a shape is the “space enclosed within the perimeter or the boundary” of the given shape. We calculate the area for different shapes using math formulas.

In the following pictures, the shaded region denotes the area for the respective shapes.

Name & Shape	Properties	Area
Circle	The length between the center “o” to the point on the circumference is the radius “r”	A = πr2 π = 3.14 (constant)
Triangle	One angle is the right angle	A = ¹⁄₂ × Base × Height
Square	All sides are equal Each angle is 90 degree	A = Length of Side²
Rhombus	All sides are equal Opposite sides are parallel Opposite angles are equal	A = p × q
Rectangle	Opposite sides are equal and parallel Each angle is 90 degree	A = Length × Breadth
Parallelogram	Opposite sides are equal and parallel Opposite angles are equal	A = Base × Height

The “textured” region represents the area of the shape

Unit of measurement

The unit of measurement for the area is always the square of the unit in which lengths are given. The resultant unit is the product of the units of the given lengths.

Let’s take an example, the area of a square with side length 8 cm is:

Area = (Length of side)²

Area = 8 cm × 8 cm

Area = 64 cm²

Application

The application field of area formula is in architecture, land surveying, and map designing. The rescaled version of the area for a given place is useful in designing knowledge tools such as globes and geophysical maps. The area calculation for a two-dimensional shape is the first step to interpret the volume of a three-dimensional object such as cone, cylinder, ball, and cube.

Fun Facts

The Babylonian clay tablets with scribes were used to study math and interpret the concept of area using formula during 1800-1600 BCE
Egyptians built great pyramids using the area based properties and ratio between the surface area of sides and base area for a perfectly balanced structure

Related math vocabulary

Circumference
Perimeter
Quadrilaterals
Circle
Irregular and regular shapes

Frequently Asked Questions

How do we find the area of irregular shapes if none of its sides are known?

To find the area of an irregular shape, divide the shape into unit squares. Count the number of squares that cover the shape completely. If the shape does not occupy complete unit squares, estimate the number of unit squares that will fill it.
Why is area a 2-dimensional quantity?

The area of any shape is the space occupied by it on a plane surface. Therefore, area is a two-dimensional quantity as well.
What is the area of a parallelogram?

Area of a parallelogram = Base × Height
What is the difference between area and volume?

The space inside the boundary of a two-dimensional shape is known as area, whereas the space occupied by a 3-dimensional object is its volume.

Area of shape - Definition with Examples

Area of Shapes

Area

Unit of measurement

Frequently Asked Questions

Practice Problems on Area of shape