Area

 

What is Area?

Area is the amount of space enclosed within the perimeter of a 2D shape.

It is measured in square units such as $mm^2$, $cm^2$, $m^2$, or $km^2$.

Example: The area of a sports field or a painting.

How to Find the Area of a Shape on a Square Grid

1. Count the total number of whole squares inside the shape.

2. Pair up half squares to form whole squares.

3. Use the given scale to determine how much area one square represents.

4. Multiply the number of squares counted by this value to find the total area.

Key Area Formulae

Area of a Rectangle: $$A = l \times w$$

where:

• l = length

• w = width

 

Area of a Triangle: $$A = \frac{1}{2}bh$$

where:

• b = base

• h = perpendicular height

 

Area of a Trapezium: $$A = \frac{1}{2}(a + b)h$$

where:

• a and b = lengths of the parallel sides

• h = perpendicular height

 

Area of a Parallelogram: $$A = bh$$

where:

• b = base

• h = perpendicular height (not the side length)

Examples

Example 1: Area of a Trapezium

• Given: a = 26 cm, b = 11 cm, h = 9 cm

 

 

$$A = \frac{1}{2}(26 + 11) \times 9$$

$$A = \frac{1}{2}(37) \times 9$$

$$A = 333 cm^2$$

 

Final Answer: 333 $cm^2$

 

Example 2: Area of a Parallelogram

• Given: b = 20 cm, h = 18 cm

 

 

$$A = 20 \times 18$$

$$A = 360 cm^2$$

 

Final Answer: 360 $cm^2$

 

Example 3: Area of a Isosceles triangle

• Given: b = 14 cm, h = 6 cm

 

 

$$A = \frac{1}{2} \times 13 \times 6$$

$$A = 39 cm^2$$

 

Final Answer: 39 $cm^2$