To find area in geometry, you measure how much space a 2D shape covers, usually in “square units” (like cm², m², in²). Below are the most common shapes and how to find their area:

Basic idea of area

  • Area is “how many unit squares” fit inside a shape.
  • It is always measured in square units (for example, if the sides are in cm, area is in cm²).
  • Different shapes use different formulas based on their sides, base, height, or radius.

Area formulas for common shapes

Rectangle

  • Formula:
    Area=length×width\text{Area}=\text{length}\times \text{width}Area=length×width

  • Example: A rectangle 5 cm by 3 cm has area 5×3=155\times 3=155×3=15 cm².

Square

  • Formula:
    Area=side×side=side2\text{Area}=\text{side}\times \text{side}=\text{side}^2Area=side×side=side2

  • Example: A square with side 4 cm has area 42=164^2=1642=16 cm².

These formulas are standard in school geometry resources.

Triangle

  • Formula:
    Area=12×base×height\text{Area}=\tfrac{1}{2}\times \text{base}\times \text{height}Area=21​×base×height

  • The base is any side; the height is the perpendicular distance to that base.

  • Example: Base 10 cm, height 6 cm → area =12×10×6=30=\tfrac{1}{2}\times 10\times 6=30=21​×10×6=30 cm².

Circle

  • Formula:
    Area=πr2\text{Area}=\pi r^2Area=πr2

  • rrr is the radius (distance from center to edge).

  • Example: Radius 3 cm → area =π×32=9π=\pi \times 3^2=9\pi =π×32=9π cm² (about 28.3 cm²).

Parallelogram and trapezoid

  • Parallelogram:
    Area=base×height\text{Area}=\text{base}\times \text{height}Area=base×height
  • Trapezoid (trapezium):
    Area=12×(base1+base2)×height\text{Area}=\tfrac{1}{2}\times (\text{base}_1+\text{base}_2)\times \text{height}Area=21​×(base1​+base2​)×height

Strategy for weird shapes

When the shape is not a standard one:

  1. Break it into simple shapes
    • Cut the shape into rectangles, triangles, or circles.
    • Find each smaller area and add them together.
  2. Or subtract
    • Find the area of a big simple shape and subtract the missing parts (holes, cutouts).
  3. Use coordinates (advanced)
    • If you know the corner coordinates, you can often split the shape into triangles or rectangles and use the usual formulas.

TL;DR

  • Learn the key formulas (rectangle, square, triangle, circle).
  • Check what measurements you are given (side, radius, base and height).
  • Either apply the formula directly, or chop the shape into simpler pieces and sum their areas.

Information gathered from public forums or data available on the internet and portrayed here.