# AREA of the Shapes Formula Explained with Clear Examples and 9 Comprehensive Video Lessons

## What is the Area of the Shapes?

A shape is defined as the figure surrounded by the closed boundary in geometry. The closed boundary consists of lines, curves and points. The amount of space inside the boundary that expresses the extent of a two-dimensional shape is defined as an area. The area is measured in square units, such as m2, cm2, mm2, km2 or ha.

The area of the shapes includes:

• rectangles
• squares
• triangles
• parallelograms
• rhombus
• kites
• trapezia, plural of trapezium
• circles
• composite shapes

## How to Handle Metric Units of Area?

### Conversion between $\text{m}^2$ and $\text{cm}^2$

\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}

## Area of Rectangles

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

## Area of Squares

\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

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

## Area of Composite Shapes 