To find area , you multiply how much space a shape covers in two directions (like length and width). The exact formula depends on the shape you have.

Quick idea of area

Area measures how much flat space is inside a shape, usually in units like cm², m², or ft².

Think of it as counting how many 1-by-1 squares fit inside the shape.

Most common shapes and formulas

Here are the key formulas people use most often.

Rectangle

  • Formula: Area=length×width\text{Area}=\text{length}\times \text{width}Area=length×width.
  • Example: A rectangle 8 cm by 2 cm has area 8×2=16 cm28\times 2=16\text{ cm}^28×2=16 cm2.

Square

  • Formula: Area=side2\text{Area}=\text{side}^2Area=side2 (side × side).
  • If each side is 5 m, area is 5×5=25 m25\times 5=25\text{ m}^25×5=25 m2.

Triangle

  • Formula: Area=12×base×height\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}Area=21​×base×height.
  • If base is 10 cm and height is 6 cm, area is 12×10×6=30 cm2\frac{1}{2}\times 10\times 6=30\text{ cm}^221​×10×6=30 cm2.

Circle

  • Formula: Area=π×r2\text{Area}=\pi \times r^2Area=π×r2, where r is the radius.
  • If radius is 7 m, area is π×72=49π≈153.94 m2\pi \times 7^2=49\pi \approx 153.94\text{ m}^2π×72=49π≈153.94 m2.

Parallelogram

  • Formula: Area=base×height\text{Area}=\text{base}\times \text{height}Area=base×height.
  • The height is the perpendicular distance between the two bases, not the slanted side.

Trapezoid (or trapezium)

  • Formula: Area=12×(base1+base2)×height\text{Area}=\frac{1}{2}\times (\text{base}_1+\text{base}_2)\times \text{height}Area=21​×(base1​+base2​)×height.
  • You average the two parallel sides, then multiply by height.

When the shape is irregular

If the shape is weird or “L‑shaped”:

  • Split it into simple shapes (rectangles, triangles, circles, trapezoids).
  • Find the area of each piece with the formulas above.
  • Add them all together to get the total area.

Example: An L‑shaped figure can be cut into two rectangles; calculate both areas then add them.

Handy HTML table of formulas

html

<table>
  <thead>
    <tr>
      <th>Shape</th>
      <th>Area formula</th>
      <th>What you need</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Rectangle</td>
      <td>Area = length × width</td>
      <td>Length, width</td>
    </tr>
    <tr>
      <td>Square</td>
      <td>Area = side²</td>
      <td>Side length</td>
    </tr>
    <tr>
      <td>Triangle</td>
      <td>Area = ½ × base × height</td>
      <td>Base, height</td>
    </tr>
    <tr>
      <td>Circle</td>
      <td>Area = π × radius²</td>
      <td>Radius</td>
    </tr>
    <tr>
      <td>Parallelogram</td>
      <td>Area = base × height</td>
      <td>Base, perpendicular height</td>
    </tr>
    <tr>
      <td>Trapezoid</td>
      <td>Area = ½ × (base₁ + base₂) × height</td>
      <td>Both bases, height</td>
    </tr>
  </tbody>
</table>

Quick 3‑step method for any problem

  1. Identify the shape (or split it into basic shapes).
  2. Write down the correct area formula from the list above.
  3. Plug in the measurements, keep units consistent, and simplify the result in square units.

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