Year 8 Unit 10: Geometry, Pythagoras and Trigonometry

Support Objectives:

• Calculate the perimeter of various shapes.

• Recall area formulae for squares, rectangles, and triangles.

• Calculate the area of compound shapes made from rectangles and triangles.
  Core Objectives:

• Recall area formulae for parallelograms and trapeziums.

• Calculate circumference and area of circles.

• Use Pythagoras' Theorem to find lengths and apply it to real life.
  Extension Objectives:

• Apply Pythagorean theorem in isosceles triangles.

• Use trigonometric ratios.

Area and Perimeter of Basic Shapes:

• Area: Space inside a shape, measured in units squared.

• Perimeter: Distance around the edge of a shape, measured in length units.

• Key Concepts:

  • Area of a triangle: $Area = \frac{b \times h}{2}$

  • Area of trapezium: $Area = \frac{(a + b) \times h}{2}$

  • Calculate area of compound shapes by summing smaller areas.
    Perimeter and Circumference of Circles:

• Key Terms:

  • Circle, radius, diameter, circumference, pi ($\pi$)

• Formulae:

  • Circumference: $C = \pi \times d$

  • Arc length: $Arc Length = \frac{\theta}{360} \times \pi \times d$

Area of Circles:

• Area of a circle: $Area = \pi \times r^2$

• Area of semicircle: $Area = \frac{\pi \times r^2}{2}$

• Area of quarter circle: $Area = \frac{\pi \times r^2}{4}$

Pythagoras' Theorem:

• Core Principle: Used to find a missing length in right-angled triangles.

• Formula: $a^2 + b^2 = c^2$

Trigonometry (Higher Level Only):

• SOHCAHTOA:

  • $\sin(\theta) = \frac{Opposite}{Hypotenuse}$

  • $\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

  • $\tan(\theta) = \frac{Opposite}{Adjacent}$

• Calculations for Angles: Use inverse functions on calculators.