About this topic
Before you begin
Calculate circular and composite areas and boundaries, recover missing dimensions, and justify angles in overlapping shapes.
Learning goals
- Calculate the area of a circle from a given radius or diameter
- Calculate the circumference of a circle from a given radius or diameter
- Calculate the enclosed area of a semicircle
- Calculate the complete perimeter of a semicircle
- Calculate the enclosed area of a quarter circle
- Calculate the complete perimeter of a quarter circle
- Calculate retained area in composite polygon and circular figures
- Calculate the complete perimeter of composite polygon and circular figures
- Find a cuboid dimension from volume and two known dimensions
- Find the edge of a cube from its volume
- Find a cuboid height from volume and base area
- Find a cuboid face area from volume and its perpendicular dimension
- Evaluate a nonnegative square root
- Evaluate a nonnegative cube root
- Use right corners and angle partitions between connected rectangles or squares
- Connect triangle, rectangle and square facts to deduce angles in a drawn composite figure
- Connect parallelogram and connected shape facts to deduce angles using existing lines
- Connect rhombus and connected shape facts to deduce angles using existing lines
- Connect trapezium and connected shape facts to deduce angles using existing lines
Syllabus statements covered
- Area and circumference of circle
- Finding the area and perimeter of
- Semicircle
- Quarter circle
- Finding the area and perimeter of composite figures made up of square, rectangle, triangle, semicircle and quarter circle
- Finding one dimension of a cuboid given its volume and the other dimensions
- Finding the length of one edge of a cube given its volume
- Finding the height of a cuboid given its volume and base area
- Finding the area of a face of a cuboid given its volume and one dimension
- Use of √ and ∛
- Finding unknown angles, without additional construction of lines, in composite geometric figures involving
- Square
- Rectangle
- Triangle
- Parallelogram
- Rhombus
- Trapezium
Choose a lesson
Work through them in order.
- Not startedCircles and composite boundariesNextUse the radius for circle area and trace every part of a composite boundary.
- Not startedAreas and boundaries of circular compositesNextChoose retained parts for area and trace complete boundaries without counting shared internal edges.
- Not startedMissing dimensions and rootsNextReverse area and volume calculations and interpret square and cube roots as lengths.
- Not startedAngles between rectangles and squaresNextUse right corners and distinguish separate gaps from overlapping corner parts.
- Not startedAngles in composite figuresNextUse marked shape properties and shared angles without inventing new lines.