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Foundation - Perimeter, area and volume

infoWhy this? We are teaching this unit so that pupils can calculate perimeter, area and volume for a range of 2D shapes and 3D solids, enabling them to tackle practical measurement problems and interpret geometric information accurately

scheduleWhy now? We are teaching it now in Year 10 so that pupils can use these measurement skills across their current GCSE topics, particularly in geometry, ratio and real-life context questions that involve composite shapes and 3D reasoning

neurologyYou need to know

  • Perimeter is the total distance around the outside of a two-dimensional shape, measured in units such as cm or m.
  • Area is the amount of surface inside a two-dimensional shape, measured in square units such as `cm^2` or `m^2`.
  • The perimeter of a polygon drawn on a square grid can be found by counting the unit lengths around its outside edge.
  • The area of a polygon drawn on a square grid can be found by counting full squares and combining part-squares to make whole squares.
  • The area of a rectangle is found using `area = length \times width`.
  • The area of a triangle is found using `area = \frac{1}{2} \times base \times height`, where the height is perpendicular to the base.
  • The area of a parallelogram is found using `area = base \times perpendicular\ height`.
  • A compound shape is a shape made from two or more basic shapes joined together.
  • The perimeter of a compound shape is found by adding only the lengths around the outside boundary of the shape.
  • The area of a trapezium is found using `area = \frac{1}{2}(a+b)h`, where `a` and `b` are the parallel sides and `h` is the perpendicular height.
  • The circumference of a circle is the distance around the circle and is found using `circumference = \pi d` or `circumference = 2\pi r`.
  • The area of a circle is found using `area = \pi r^2`, where `r` is the radius.
  • A semicircle is half of a circle, so its area is `\frac{1}{2}\pi r^2` and its curved arc length is `\frac{1}{2}\times 2\pi r`.
  • A quarter-circle is one quarter of a circle, so its area is `\frac{1}{4}\pi r^2` and its curved arc length is `\frac{1}{4}\times 2\pi r`.
  • Volume is the amount of three-dimensional space inside a solid, measured in cubic units such as `cm^3` or `m^3`.
  • The volume of a cuboid is found using `volume = length \times width \times height`.
  • The volume of a prism is found using `volume = area\ of\ cross\text{-}section \times length`.
  • A cylinder is a prism-like solid with a circular cross-section, and its volume is found using `volume = \pi r^2 h`.
  • Surface area is the total area of all the faces of a three-dimensional solid, measured in square units.
  • The surface area of a prism is found by adding the areas of all its faces, including the two congruent cross-sections and the rectangular side faces.

rocket_launchYou must be able to

  • Calculate the perimeter of a polygon on a square grid by counting each unit length around the outside exactly once.
  • Calculate the area of a grid-based polygon by counting full squares and combining matching part-squares to make whole squares.
  • Calculate the area of rectangles, triangles, parallelograms and trapezia by selecting the correct formula and using the perpendicular height where required.
  • Find the perimeter of a compound shape by identifying any missing side lengths and adding only the exterior side lengths.
  • Calculate the area of a compound shape by splitting it into basic shapes, finding each area, and adding or subtracting areas as appropriate.
  • Calculate the area and circumference of circles and part-circles by substituting the correct radius or diameter into the circle formulae and including straight edges when finding perimeter.
  • Calculate the volume of cubes, cuboids, triangular prisms and other prisms by finding the cross-sectional area and multiplying by the prism length.
  • Calculate the volume of a cylinder by finding the circular cross-sectional area and multiplying by the height.
  • Calculate the surface area of cuboids and triangular prisms by finding the area of every face and adding the areas without duplication.


Revision Quiz

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