Area of Common Shapes: Calculator & Guide

Understanding Area

Area is a measure of the amount of two-dimensional space a shape occupies. It's expressed in square units.

SI Unit of Area

The standard SI (International System of Units) unit for area is the square meter, denoted as $m^2$. Other common units include square centimeters ($cm^2$), square kilometers ($km^2$), square inches ($in^2$), and square feet ($ft^2$).

Common Polygons

Polygons are two-dimensional closed shapes made of straight line segments. They are named based on the number of sides they have:

Triangle: A polygon with 3 sides.
Quadrilateral: A polygon with 4 sides.
Pentagon: A polygon with 5 sides.
Hexagon: A polygon with 6 sides.
Heptagon (or Septagon): A polygon with 7 sides.
Octagon: A polygon with 8 sides.

Common Quadrilaterals

Quadrilaterals are polygons with four sides. Some common types include:

Rectangle: A quadrilateral with four right angles ($90^\circ$). Opposite sides are equal in length and parallel.
Square: A special type of rectangle where all four sides are equal in length. It also has four right angles.
Parallelogram: A quadrilateral with two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal.
Rhombus: A parallelogram where all four sides are equal in length. Opposite angles are equal, and its diagonals bisect each other at right angles.
Trapezium (or Trapezoid): A quadrilateral with at least one pair of parallel sides. These parallel sides are called bases.

Area Calculators

Select a shape below to calculate its area. Enter the required dimensions and click "Calculate".

Triangle

Formula: $A = \frac{1}{2} \times \text{base} \times \text{height}$

Base (b): Height (h):

Result will appear here.

Rectangle

Formula: $A = \text{length} \times \text{width}$

Length (l): Width (w):

Result will appear here.

Square

Formula: $A = \text{side}^2$

Side (s):

Result will appear here.

Parallelogram

Formula: $A = \text{base} \times \text{height}$

Base (b): Height (h):

Result will appear here.

Rhombus

Formula: $A = \frac{1}{2} \times d_1 \times d_2$ (using diagonals)

Diagonal 1 ($d_1$): Diagonal 2 ($d_2$):

Result will appear here.

Trapezium (Trapezoid)

Formula: $A = \frac{1}{2} \times (a+b) \times h$

Base 1 (a): Base 2 (b): Height (h):

Result will appear here.

Circle

Formula: $A = \pi \times r^2$ (where $\pi \approx 3.14159$)

Radius (r):

Result will appear here.

Ellipse

Formula: $A = \pi \times a \times b$

Semi-major axis (a): Semi-minor axis (b):

Result will appear here.

Sector of a Circle

Formula: $A = \frac{\theta}{360^\circ} \times \pi \times r^2$ (angle $\theta$ in degrees)

Radius (r): Angle ($\theta$) in degrees:

Result will appear here.

Areas of Similar Shapes

Similar shapes are shapes that have the same form but may differ in size. Their corresponding angles are equal, and the ratio of their corresponding linear dimensions (like sides, heights, radii) is constant.

A key property is that the ratio of the areas of two similar shapes is equal to the square of the ratio of their corresponding linear dimensions. If $L_1$ and $L_2$ are corresponding linear dimensions of two similar shapes, and $A_1$ and $A_2$ are their respective areas, then:

$\frac{A_1}{A_2} = \left(\frac{L_1}{L_2}\right)^2$

This means if you double the side length of a square, its area becomes $2^2 = 4$ times larger. If you triple the radius of a circle, its area becomes $3^2 = 9$ times larger.