Standard Measurement – Perimeter, area and volume

This lesson comprises two (2) master classes focusing on:

• Perimeter and area of 2D shapes
• Surface area and volume of 3D shapes
• Pythagoras’ theorem
• Trapezoidal rule

Content:

MS-M1.2

• Review and extend how to solve practical problems requiring the calculation of perimeters and areas of triangles, rectangles, parallelograms, trapezia, circles, sectors of circles and composite shapes
  • review the use of Pythagoras’ theorem to solve problems involving right-angled triangles
  • review the use of a scale factor to find unknown lengths in similar figures
• Solve problems involving surface area of solids including prisms, cylinders, spheres and composite solids
• Solve problems involving volume and capacity of solids including prisms, cylinders, spheres, pyramids and composite solids
  • convert between units of volume and capacity
• Calculate perimeters and areas of irregularly shaped blocks of land by dissection into regular shapes including triangles and trapezia
  • derive the Trapezoidal rule for a single application, \( A \approx \frac{h}{2}(d_f+d_l) \)
  • use the Trapezoidal rule to solve a variety of practical problems with and without technology, eg the volume of water in a swimming pool
• Solve problems involving perimeters, area, surface area, volumes and capacity in a variety of contexts