Area of a Shape – Definition with 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 equalEach angle is 90 degree	A = Length of Side2
Rhombus	All sides are equalOpposite sides are parallelOpposite angles are equal	A = p × q
Rectangle	Opposite sides are equal and parallelEach angle is 90 degree	A = Length × Breadth
Parallelogram	Opposite sides are equal and parallelOpposite 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 1. The Babylonian clay tablets with scribes were used to study math and interpret the concept of area using formula during 1800-1600 BCE. 2. 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

Practice Problems

Area of Shape Attend this Quiz & Test your knowledge. 1What is the area of a parallelogram with a base of 4 cm and a height 3 cm more than its base? 12 square cm 14 square cm 24 square cm 28 square cm CorrectIncorrect Correct answer is: 28 square cm The height of the parallelogram = base + 3 cm, i.e., 4 cm + 3 cm or 7 cm. So, the area of the parallelogram = base ✕ height = 7 cm ✕ 4 cm or 28 square cm. 2What is the area of a rectangle with a width of 5 units and a length double its width? 25 square units 30 square units 50 square units 100 square units CorrectIncorrect Correct answer is: 50 square units The length of the rectangle = 2 ✕ width, i.e., 2 ✕ 5 units or 10 units. So, Area of the rectangle = length ✕ width = 10 units ✕ 5 units or 50 square units. 3What is the area of a shape made by joining three squares of side 3 cm? 6 square cm 9 square cm 18 square cm 27 square cm CorrectIncorrect Correct answer is: 27 square cm The area of a square is side ✕ side, i.e., 3 cm ✕ 3 cm or 9 square cm. So, the area of 3 such squares will be 3 ✕ 9 square cm or 27 square cm. 4What is the formula for the area of a circle with radius r? 𝜋 ✕ r 2 ✕ 𝜋 ✕ r 𝜋 ✕ r ✕ r 2 ✕ 𝜋 ✕ r ✕ r CorrectIncorrect Correct answer is: 𝜋 ✕ r ✕ r The area of a circle is 𝜋 ✕ radius ✕ radius.