Area of 2D Shapes
Maths: Edexcel IGCSE Higher, topic 4.7.3
Area of a Triangle
We can use the formula: area of a triangle = 1⁄2ab sin(C).
Formula
- Area of a triangle = 1⁄2ab sin(C) since the vertical height is b sin(C).
- This formula can also be used to calculate the side length of a triangle whose area is known.
Example
- If we are given a triangle with two sides of 8cm and 10cm and the area is 20cm2, we can calculate the angle between the sides as follows:
- 20 = 1⁄2 × 8 × 10 × sin(C)
- 20 = 40 × sin(C)
- sin(C) = 1⁄2
- C = 30°
Calculating Area of 2D Shapes
We can use formulae to calculate the area of common shapes.
Triangle
- Area = 1⁄2 × base × vertical height.
Parallelogram
- Area = base × vertical height.
Trapezium
- Area = 1⁄2 × (a + b) × vertical height.
Fractions of Circles
Arc length
- An arc length is a fraction of the circumference of the circle:
- Arc length = angle⁄360 × circumference of circle
- Arc length = angle⁄360 × 2πr
Area of a sector
- The area of a sector is a fraction of the area of the circle:
- Area of sector = angle⁄360 × πr2
Area of a segment
- To find the area of a segment, find the area of the full sector and subtract the area of the triangle using the formula:
- Area of triangle = 1⁄2 × ab × sin(C)
- Therefore:
- Area of segment = (angle⁄360 × πr2) - (1⁄2 × ab × sin(C))
Test yourself on Area of 2D Shapes
Which is the correct formula for the area of a triangle?
What is the correct formula for the area of a parallelogram?
What is the correct formula for the area of a trapezium?
What is the correct formula for the area of a triangle?