CIE IGCSE Mathematics (0580) Area and perimeter Study Notes - New Syllabus
CIE IGCSE Mathematics (0580) Area and perimeter Study Note
LEARNING OBJECTIVE
- Perimeter and Area of 2D Shapes
Key Concepts:
- Perimeter and Area of 2D Shapes
Perimeter and Area of 2D Shapes
Rectangle
A rectangle is a quadrilateral with four right angles and opposite sides equal.
Properties of Rectangle
- Has 4 right angles (each 90°).
- Opposite sides are equal and parallel.
- Diagonals are equal and bisect each other.
$\mathrm{Area = length \times width}$
$\mathrm{Perimeter = 2 \times (length + width)}$
Example:
A rectangle is 8 cm long and 5 cm wide. Find its area and perimeter.
▶️ Answer/Explanation
Area = \( 8 \times 5 = 40 \ \text{cm}^2 \)
Perimeter = \( 2 \times (8 + 5) = 2 \times 13 = 26 \ \text{cm} \)
Example:
The perimeter of a rectangle is 30 cm and its length is 9 cm. Find its width.
▶️ Answer/Explanation
\( 2(l + w) = 30 \Rightarrow l + w = 15 \Rightarrow 9 + w = 15 \Rightarrow w = 6 \ \text{cm} \)
Triangle
A triangle is a polygon with three sides and three angles.
Properties of Triangle
- Has 3 sides and 3 angles.
- The sum of interior angles is always 180°.
- Can be classified as scalene, isosceles, or equilateral.
$\text{Area =}$ \( \frac{1}{2} \times \text{base} \times \text{height} \)
$\mathrm{Perimeter = sum~of~all~sides}$
Example:
A triangle has base 10 cm and height 6 cm. Find its area.
▶️ Answer/Explanation
Area = \( \frac{1}{2} \times 10 \times 6 = 30 \ \text{cm}^2 \)
Example:
A triangle has sides 7 cm, 8 cm and 9 cm. Find its perimeter.
▶️ Answer/Explanation
Perimeter = \( 7 + 8 + 9 = 24 \ \text{cm} \)
Parallelogram
A parallelogram is a quadrilateral with opposite sides equal and parallel.
Properties of Parallelogram
- Opposite sides are equal and parallel.
- Opposite angles are equal.
- Diagonals bisect each other.
$\mathrm{Area = base \times height}$
$\mathrm{Perimeter = 2 \times (base + side)}$
Example:
A parallelogram has base 12 cm and height 5 cm. Find its area.
▶️ Answer/Explanation
Area = \( 12 \times 5 = 60 \ \text{cm}^2 \)
Example:
The base and side of a parallelogram are 10 cm and 7 cm. Find the perimeter.
▶️ Answer/Explanation
Perimeter = \( 2 \times (10 + 7) = 2 \times 17 = 34 \ \text{cm} \)
Trapezium
A trapezium is a quadrilateral with one pair of opposite sides parallel.
Properties of Trapezium
- Has one pair of opposite sides that are parallel (called bases).
- May be isosceles if non-parallel sides are equal.
- Height is the perpendicular distance between the parallel sides.
$\mathrm{Area =}$ \( \frac{1}{2} \times (\text{a} + \text{b}) \times \text{height} \), where a and b are the parallel sides
$\mathrm{Perimeter = sum~of~all~sides}$
Example:
Find the area of a trapezium with parallel sides 10 cm and 6 cm, and height 5 cm.
▶️ Answer/Explanation
Area = \( \frac{1}{2} \times (10 + 6) \times 5 = \frac{1}{2} \times 16 \times 5 = 40 \ \text{cm}^2 \)
Example:
Find the perimeter of a trapezium with sides 6 cm, 5 cm, 4 cm, and 7 cm.
▶️ Answer/Explanation
Perimeter = \( 6 + 5 + 4 + 7 = 22 \ \text{cm} \)