What is Area in Math? – Area Definition

Simply put, area is the amount of space a flat surface or shape covers. In other words, it measures the size of a surface.

A helpful way to understand area is to imagine how much paint would be needed to completely cover a shape. For example, if you had several different shapes that each needed the same amount of paint to fill them, they would all have the same area — even if they look very different!

➡️ Example: All the shapes below cover 12 square units, even though they are different in shape.

How to Calculate Area?

The way you calculate area depends on the shape you’re dealing with. Each shape has its own formula.

Below, we’ve listed the area formulas for different shapes that our area calculator supports. For simplicity, we’re only showing the equations here. You can find diagrams, detailed explanations, and step-by-step guides in the sections dedicated to each shape (or in specific tools made for them).

1. Rectangle

A rectangle has four right angles.
Area formula:
Area = length × width

Example:
A farmer has a rectangular plot:

• Length = 220 ft

• Width = 99 ft

• Area = 220 × 99 = 21,780 square feet

This is roughly half an acre. Despite its size, foreign investors weren’t impressed — they wanted more square feet for their money!

2. Triangle

To find the area of a triangle when all three sides are known, we use Heron’s Formula:

Example:
The farmer builds a triangular pool for his daughter, using sides of 77 ft each (equilateral).

• s = (77 + 77 + 77)/2 = 115.5

• Area = √[115.5(115.5 − 77)³] ≈ 2,567.33 sq ft

His daughter, obsessed with triangles, is thrilled.

3. Trapezoid

A trapezoid has one pair of parallel sides.
Area formula:
Area = (b₁ + b₂)/2 × height

Example:
The farmer builds a ramp:

• Bottom base = 29.528 ft

• Top base = 9 ft

• Height = 9 ft

• Area = (29.528 + 9)/2 × 9 ≈ 173.38 sq ft

This ramp helps his daughter practice BMX tricks.

4. Circle

A circle’s area depends on its radius.
Area formula:
Area = π × r²

Example:
The daughter makes a crop circle prank:

• Radius = 15 ft

• Area = π × 15² ≈ 706.86 sq ft

Aliens or not, it scares the farmer and damages his crops.

5. Sector (Pie Slice of a Circle)

Area formula (θ in degrees):
Area = (θ/360) × π × r²

Example:
They bake a 16-inch radius pie. The raccoon eats half (180°)!

• Remaining = 180°

• Each of 3 people gets 60°

• Area per slice = (60/360) × π × 16² ≈ 134.04 in²

Platypus the raccoon is full. Everyone else gets less pie.

6. Ellipse

An ellipse is like a stretched circle.
Area formula:
Area = π × a × b
(where a and b are semi-major and semi-minor axes)

FAQs

Q1. What is area?
A: Area is the amount of space inside a flat surface or shape. It’s measured in square units like square meters (m²), square feet (ft²), or square inches (in²).

Q2. How do you calculate the area of a rectangle?
A: Multiply the length by the width:
Area = length × width

Q3. What is the formula for the area of a triangle when all three sides are known?
A: Use Heron’s Formula:

• s = (x + y + z) / 2

• Area = √[s(s − x)(s − y)(s − z)]
  Where x, y, and z are the side lengths.

Q4. How do you find the area of a trapezoid?
A: Use this formula:
Area = (base₁ + base₂) / 2 × height
Base₁ and base₂ are the parallel sides.

Q5. How is the area of a circle calculated?
A: Use this formula:
Area = π × r², where r is the radius.

Q6. What’s the formula for the area of a sector (part of a circle)?
A: If the angle is in degrees:
Area = (θ / 360) × π × r²
Where θ is the angle of the sector and r is the radius.

Q7. How do you calculate the area of an ellipse?
A: Use this formula:
Area = π × a × b
Where a is the semi-major axis and b is the semi-minor axis.

Q8. Why is understanding area important in real life?
A: Knowing how to calculate area helps in farming, construction, interior design, land measurement, and even baking — anytime you need to measure or compare spaces.