The Ultimate Guide to Shape Area Formulas and Calculations

Area of Shapes Formula Explained

What is the Area of the Shapes?

Understanding how to calculate the area of various shapes is a fundamental skill in geometry. In this article, we’ll explore the formulas for calculating the area of common shapes and provide tips for handling metric unit conversions.

What is Area?

Area is the amount of space within the boundaries of a two-dimensional shape. It is measured in square units, such as m², cm², mm², km², or ha. Shapes can be defined by closed boundaries consisting of lines, curves, and points.

Formulas for Common Shapes

To calculate the area of a shape, you’ll need to use the appropriate formula. Here are the formulas for some common shapes:

  • Rectangles: A = length × width
  • Squares: A = side length²
  • Triangles: A = (base × height) ÷ 2
  • Parallelograms: A = base × height
  • Rhombus: A = (diagonal 1 × diagonal 2) ÷ 2
  • Kites: A = (diagonal 1 × diagonal 2) ÷ 2
  • Trapezia: A = ((top base + bottom base) × height) ÷ 2
  • Circles: A = π × radius²

Composite shapes can be broken down into simpler shapes, and their areas can be calculated by adding or subtracting the areas of the individual shapes.

How to Handle Metric Units of Area?

Conversion between \( \text{m}^2 \) and \( \text{cm}^2 \)

When working with area calculations, it’s essential to be comfortable with metric unit conversions. Some common conversions include:

\( \begin{align} \text{1 m}^2 &= \text{100 cm} \times \text{100 cm} = \text{10 000 cm}^2 \\ \text{2 m}^2 &= 2 \times \text{10 000 cm}^2 = \text{20 000 cm}^2 \\ \text{500 cm}^2 &= 500 \div \text{10 000 m}^2 = \text{0.05 m}^2 \end{align} \)

Conversion between \( \text{m}^2 \) and \( \text{km}^2 \)

\( \begin{align} \text{1 km}^2 &= \text{1000 m} \times \text{1000 m} = \text{1000 000 m}^2 \\ \text{3 km}^2 &= 3 \times \text{1000 000 m}^2 = \text{3000 000 m}^2 \\ \text{1200 m}^2 &= 1200 \div \text{1000 000 km}^2 = \text{0.0012 km}^2 \end{align} \)

Conversion between \( \text{m}^2 \) and \( \text{mm}^2 \)

\( \begin{align} \text{1 m}^2 &= \text{1000 mm} \times \text{1000 mm} = \text{1000 000 mm}^2 \\ \text{3.1 m}^2 &= 3.1 \times \text{1000 000 mm}^2 = \text{3100 000 mm}^2 \\ \text{5600 mm}^2 &= 5600 \div \text{1000 000 m}^2 = \text{0.0056 m}^2 \end{align} \)

Conversion between \( \text{cm}^2 \) and \( \text{mm}^2 \)

\( \begin{align} \text{1 cm}^2 &= \text{10 mm} \times \text{10 mm} = \text{100 mm}^2 \\ \text{3.1 cm}^2 &= 3.1 \times \text{100 mm}^2 = \text{310 mm}^2 \\ \text{86 000 mm}^2 &= 86 \ 000 \div \text{100 cm}^2 = \text{860 cm}^2 \end{align} \)

Conversion between \( \text{m}^2 \) and \( \text{ha} \)

\( \begin{align} \text{1 ha} &= \text{100 m} \times \text{100 m} = \text{10 000 m}^2 \\ \text{3.4 ha} &= 3.4 \times \text{10 000 m}^2 = \text{34 000 m}^2 \\ \text{45 000 m}^2 &= 45 \ 000 \div \text{10 000 ha} = \text{4.5 ha} \end{align} \)

Conversion between \( \text{km}^2 \) and \( \text{ha} \)

\( \begin{align} \text{1 km}^2 &= \text{1000 m} \times \text{1000 m} = \text{1000 000 m}^2 = 100 \times \text{10 000 m}^2 = \text{100 ha} \\ \text{1.23 km}^2 &= 1.23 \times \text{100 ha} = \text{123 ha} \\ \text{450 ha} &= 450 \div \text{100 km}^2 = \text{4.5 km}^2 \end{align} \)

By mastering these conversions and applying the appropriate formulas, you’ll be able to accurately calculate the area of any shape in various metric units.


Calculating the area of shapes is a valuable skill that has numerous applications in geometry, engineering, and everyday life. By familiarizing yourself with the formulas for common shapes and practising metric unit conversions, you’ll be well-equipped to tackle any area calculation problem with confidence.


Area of Rectangles

Area of Rectangles

$$ \text{Area of a Rectangle} = \text{base} \times \text{height} $$


Area of Squares

Area of a square

$$ \begin{align} \text{Area of a Square} &= \text{side} \times \text{side} \\ &= \text{side}^2 \end{align} $$


Area of Triangles

$$ \text{Area of a Triangle} = \displaystyle \frac{1}{2} \times \text{base} \times \text{height} $$


Area of Parallelograms

parallelogram

$$ \text{Area of a Rectangle} = \text{base} \times \text{height} $$


Area of Rhombus and Kites


Area of Trapezia


Area of Circles


Area of Composite Shapes

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