Geometry and Measures Depth
Geometry and Measures Depth extends KS2 geometry to plotting and reading coordinates in all four quadrants, reflecting and translating shapes on a coordinate grid, finding the area and perimeter of compound 2D shapes, and finding the volume of a cuboid by multiplying length by width by height.
Before you start
Make sure you're comfortable with these topics first:
Method
- Plot and read coordinates in the order (x, y): the x-coordinate first (across), then the y-coordinate (up or down), remembering negative coordinates sit to the left of or below the origin.
- To reflect a shape in a mirror line, measure each vertex's perpendicular distance from the line and plot the same distance on the opposite side.
- To translate a shape, move every vertex the same number of squares right or left and up or down; the shape's size and orientation never change.
- To find the area of a compound shape, split it into rectangles, find the area of each rectangle (length x width), then add the areas together.
- To find the perimeter of a compound shape, add up the length of every outside edge, working out any missing side lengths first.
- To find the volume of a cuboid, multiply its length by its width by its height, giving the answer in cubic units.
- Learn that the diameter of a circle is exactly twice its radius, and both are measured from or through the centre.
Worked example
An L-shaped room is made from a 6m by 4m rectangle with a 2m by 3m rectangle removed from one corner. Work out the area of the room.
- Find the area of the full large rectangle: 6 x 4 = 24 square metres.
- Find the area of the rectangle that has been removed: 2 x 3 = 6 square metres.
- Subtract the removed area from the full rectangle's area: 24 - 6 = 18.
- So the area of the L-shaped room is 18 square metres.
Practice questions
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Q1Write the coordinates of a point that is 3 to the left and 2 down from the origin.Show answer
Answer: (-3, -2)
Q2A shape is translated 4 squares right and 2 squares up. If a vertex starts at (1, 1), where is it now?Show answer
Answer: (5, 3)
Q3A cuboid has length 5cm, width 3cm and height 2cm. Work out its volume.Show answer
Answer: 30 cubic cm
Q4A circle has a radius of 6cm. What is its diameter?Show answer
Answer: 12cm
Q5A rectangle 10cm by 4cm has a 2cm by 4cm rectangle cut from one corner. What is the remaining area?Show answer
Answer: 32 square cm (40 - 8)
Q6Reflect the point (3, 2) in the y-axis (the line x = 0). What are the new coordinates?Show answer
Answer: (-3, 2)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A compound shape is made from an 8cm by 5cm rectangle with a 3cm by 2cm rectangle removed from one corner. Work out the area of the compound shape.
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A cuboid-shaped box has a length of 12cm, a width of 5cm and a height of 4cm. a) Work out the volume of the box. b) A second box has the same length and width but double the height. Work out the volume of the second box.
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Free printable worksheet
Want more practice on paper? Download the geometry and measures depth worksheet pack - 12 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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