how to find area
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
- Identify the shape (or split it into basic shapes).
- Write down the correct area formula from the list above.
- 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.