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Area Calculator

Calculate the area of 16 different geometric shapes with step-by-step solutions

Calculate Area

A quadrilateral with four right angles and opposite sides equal

Area Results

0.000000
m²
Formula Used
A = length × width

Area in Different Units

0.000e+0
mm²
0.000e+0
cm²
0.000e+0
m²
0.000e+0
km²
0.000e+0
in²
0.000e+0
ft²
0.000e+0
yd²
0.000e+0
mi²
0.000e+0
acres
0.000e+0
hectares

How to Calculate Rectangle Area

Formula: A = length × width

A quadrilateral with four right angles and opposite sides equal

Example: Rectangle Area Calculation

Problem

Find the area of a rectangle with length = 8 meters and width = 5 meters

Solution

Step 1: Identify the formula: A = length × width

Step 2: Substitute values: A = 8 × 5

Step 3: Calculate: A = 40 square meters

Answer: The area is 40 m²

Common Area Formulas

Rectangle: A = l × w
Square: A = s²
Triangle: A = ½bh
Circle: A = πr²
Parallelogram: A = bh
Trapezoid: A = ½(a+b)h
Regular Polygon: A = (n×s²×cot(π/n))/4

Unit Conversion

1 m² =10,000 cm²
1 m² =10.764 ft²
1 ft² =144 in²
1 acre =4,047 m²
1 hectare =10,000 m²

Area Calculation Tips

✓

Always use the same units for all measurements

✓

For irregular shapes, divide into simpler shapes

✓

Double-check your measurements before calculating

✓

Use appropriate precision for your application

Understanding Area in Mathematics

What is Area?

Area is a measure of the amount of space inside a two-dimensional shape. It's expressed in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²). Think of area as the amount of paint needed to cover a surface.

Key Concepts

  • •Base: The bottom edge of a shape
  • •Height: The perpendicular distance from base to top
  • •Radius: Distance from center to edge of a circle
  • •Diagonal: A line connecting opposite vertices

Area Applications

  • •Construction: Calculating materials needed
  • •Real Estate: Determining property sizes
  • •Agriculture: Planning crop areas
  • •Interior Design: Flooring and painting

Special Cases

Heron's Formula: Calculates triangle area using only side lengths

Regular Polygons: Use symmetry for simplified calculations

Composite Shapes: Break down into simpler shapes and add areas

Area Formulas by Shape Category

Quadrilaterals

  • Rectangle: l × w
  • Square: s²
  • Parallelogram: b × h
  • Rhombus: ½ × d₁ × d₂
  • Trapezoid: ½(a + b) × h

Curved Shapes

  • Circle: πr²
  • Ellipse: πab
  • Sector: ½r²θ
  • Annulus: π(R² - r²)

Polygons

  • Triangle: ½bh
  • Pentagon: ¼√(25+10√5)s²
  • Hexagon: (3√3/2)s²
  • Octagon: 2(1+√2)s²

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