# The Ultimate Guide to Shape Area Formulas and Calculations

## 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 mÂ², cmÂ², mmÂ², kmÂ², 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 Ã— width
- Squares: A = side lengthÂ²
- Triangles: A = (base Ã— height) Ã· 2
- Parallelograms: A = base Ã— height
- Rhombus: A = (diagonal 1 Ã— diagonal 2) Ã· 2
- Kites: A = (diagonal 1 Ã— diagonal 2) Ã· 2
- Trapezia: A = ((top base + bottom base) Ã— height) Ã· 2
- Circles: A = Ï€ Ã— radiusÂ²

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

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

## 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 Rhombus and Kites

## Area of Trapezia

## Area of Circles

## Area of Composite Shapes

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