Areas- Triangles and Quadrilaterals

Areas- Triangles and Quadrilaterals

Understanding Triangles and Quadrilaterals

  • Get to know what a triangle and a quadrilateral is: a triangle is a shape with three straight sides and a quadrilateral is a shape with four straight sides.

  • Understand that triangles can be classified into several types based on their sides and angles: equilateral (all sides equal), isosceles (two sides equal), scalene (no sides equal), acute (all angles less than 90 degrees), obtuse (one angle greater than 90 degrees), right (one angle equal to 90 degrees).

  • Recognise that quadrilaterals can be of several types: paralellogram (opposite sides equal and parallel), rectangle (parallelogram with a right angle), square (rectangle with all sides equal), trapezium (at least one pair of parallel sides), rhombus (parallelogram with all sides equal), kite (two pair of adjacent sides equal).

Calculating Areas of Triangles and Quadrilaterals

  • Recall the fundamental formula to calculate the area of a triangle which is 1/2 x base x height.

  • Realise that the base and height of a triangle must be perpendicular to each other.

  • In the case of a right triangle, you can directly use the two sides forming the right angle as your base and height.

  • Understand that the formula to calculate the area of a quadrilateral depends on its type.

  • Rectangle: length x width
  • Square: side^2
  • Parallelogram: base x height (height is perpendicular to the base)
  • Trapezium: 1/2 x sum of parallel sides x height (height is perpendicular to the parallel sides)

Problem Solving with Areas

  • Apply your knowledge of areas for practical problem solving.

  • Problems can often involve finding a missing side given the area and the other side (or height).

  • Complex problems may require the use of Pythagoras’ theorem or trigonometry along with area formulas.

Using Area Knowledge in Composite Shapes

  • Understand how to find the area of composite shapes made up of triangles and quadrilaterals by breaking them down into simpler shapes.

  • Note that finding the area of unknown or irregular shapes often involves dividing the shape into known regular shapes.

  • Apply your problem-solving skills to calculate the area of the unknown shape using the formulas you know.