Calculating Area

The formula for calculating area depends on the shape. For example, to calculate the area of a rectangle or square, you multiply the length by the width. To calculate the area of a circle, you use the formula A = 𝜋r².

Calculating area for different shapes

Rectangle or square: Multiply the length by the width
Circle: Use the formula A = 𝜋r²
Triangle: Use the SSS, SAS, SSA, or ASA method, depending on which side or angle measurements you know
Parallelogram: Multiply the width by the height
Hexagon: Use the formula Hexagon Area = 3/2 × √3 × a², where a is the side of the hexagon
Rhomboid: Multiply the base by the height

When to calculate area

You can use area calculations in many real-world situations, such as when carpeting a room, painting a wall, or building a road.

Example

Calculating Area of Different Shapes

Area calculation is a fundamental concept in geometry used to determine the surface occupied by a two-dimensional shape. The formula used depends on the type of shape.

The general approach to calculating the area includes:

Identifying the shape (e.g., rectangle, triangle, circle, etc.).
Using the appropriate mathematical formula for the shape.
Substituting given values and computing the result.

Calculating the Area of a Rectangle

A rectangle is a four-sided shape with opposite sides equal. The formula for its area is:

\[ A = l \times w \]

Example:

If the length is 10 cm and the width is 5 cm, the area is:

Step 1: Multiply length and width: \( 10 \times 5 \).
Step 2: Compute the result: \( A = 50 \) cm².

Calculating the Area of a Triangle

A triangle is a three-sided shape, and its area is given by:

\[ A = \frac{1}{2} \times b \times h \]

Example:

If the base is 8 cm and the height is 6 cm, the area is:

Step 1: Multiply base and height: \( 8 \times 6 \).
Step 2: Divide by 2: \( A = \frac{48}{2} = 24 \) cm².

Calculating the Area of a Circle

A circle is a round shape, and its area is given by:

\[ A = \pi r^2 \]

Example:

If the radius is 7 cm, the area is:

Step 1: Square the radius: \( 7^2 = 49 \).
Step 2: Multiply by \( \pi \) (≈3.14): \( A = 3.14 \times 49 = 153.86 \) cm².

Real-life Applications of Area Calculation

Calculating area has many practical applications, such as:

Determining the amount of paint needed to cover a wall.
Calculating the amount of material required for flooring.
Estimating land sizes for agricultural and construction purposes.

Common Area Formulas

Rectangle: \( A = l \times w \)

Triangle: \( A = \frac{1}{2} \times b \times h \)

Circle: \( A = \pi r^2 \)

Additional Shapes: Other shapes like trapezoids, parallelograms, and sectors of circles have specific formulas that involve their dimensions and angles.

Area Calculation Examples Table
Shape	Description	Formula	Example Calculation
Rectangle	A quadrilateral with opposite sides equal.	Area = length × width	For a rectangle with length 5m and width 3m: \( 5 \times 3 = 15m^2 \).
Triangle	A three-sided polygon.	Area = (base × height) ÷ 2	For a triangle with base 6m and height 4m: \( (6 \times 4) \div 2 = 12m^2 \).
Circle	A round shape with all points equidistant from the center.	Area = π × radius²	For a circle with radius 7m: \( \pi \times 7^2 = 153.94m^2 \) (approx).
Trapezium	A quadrilateral with one pair of parallel sides.	Area = ((base1 + base2) × height) ÷ 2	For a trapezium with bases 8m and 6m, and height 5m: \( ((8 + 6) \times 5) \div 2 = 35m^2 \).