Imaginesis: printable Year 5 Properties of Shapes maths worksheets for England (National Curriculum) — Finding the Area and Missing Sides of Rectangles, Classifying Acute, Obtuse, and Reflex Angles, Finding Missing Angles: word problems with hints, answers and worked solutions as PDF, also as an A/B test.
By the orchard hedge, Kai builds an automatic drip system to water a rectangular garden bed. The bed is 13 m long and 4 m wide. How many square metres does this garden bed cover?
Hint: Think about the rectangular garden bed as a grid made of rows and columns. Picture 4 rows of one-metre squares along the width, with 13 metres in each row, and find how many square metres that makes in all.
Answer: 52 m²
Felix checks the metal pointer on the bird ring sorting table at the field station. He adjusts the pointer until the dial shows an angle of 25 degrees. Is this angle acute, right, obtuse, or straight?
Hint: Compare the pointer's angle of 25 degrees to 90 degrees and 180 degrees to determine which type of angle it is.
Answer: acute angle
Ben turns the round dial of the oven timer across an angle of 90 degrees to start the soup. The dial turns through 50 degrees before he pauses to add the carrots. How many degrees are left to turn?
Hint: Start with the total angle of 90 degrees on the oven dial, then subtract the 50 degrees that Ben has already turned.
Answer: 40°
Children learn to calculate the area of rectangles in cm² and m², and work backwards from the area to find an unknown side length.
Y5.GPS.5 use the properties of rectangles to deduce related facts and find missing lengths and anglesY5.M.4 calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapesY6.M.4 recognise that shapes with the same areas can have different perimeters and vice versaY6.M.5 recognise when it is possible to use formulae for area and volume of shapes
In Year 5, children calculate and compare the area of rectangles and squares using standard units, specifically square centimetres (cm²) and square metres (m²). They multiply the length by the width to determine the total space inside a shape. Children also use short division to reverse this calculation: using a known area and one given side to deduce the missing length of another side.
A frequent mistake is mixing up area and perimeter. Pupils often add the side lengths together instead of multiplying them, or label their final answer with standard units like cm rather than square units like cm². When finding an unknown side, children also commonly try to multiply the area by the known measurement instead of dividing the area by that side.
Worksheet tasks build this skill step by step. With Area of a rectangle, children calculate the area from labelled diagrams, while Area of a rectangle in everyday life applies these calculations to real-world contexts such as garden plots or tabletop measurements. In Missing side of a rectangle tasks, children are presented with the total area alongside one dimension and must divide to find the missing edge.
Children learn to classify angles by their degree measurements as acute, right, obtuse, or reflex using turns and multiples of 90 degrees.
Y3.GPS.2 recognise angles as a property of shape or a description of a turnY3.GPS.3 identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angleY4.GPS.2 identify acute and obtuse angles and compare and order angles up to two right angles by sizeY5.GPS.2 know angles are measured in degrees: estimate and compare acute, obtuse and reflex anglesY5.GPS.4.c other multiples of 90°
In Year 5, children build on their knowledge of right angles and turns to classify angles measured in degrees. They learn to identify whether an angle is acute (less than 90°), a right angle (exactly 90°), obtuse (between 90° and 180°), or reflex (greater than 180° but less than a full 360° turn).
A common mistake occurs when identifying reflex angles on paper. Children often focus on the smaller interior angle between the two lines rather than the curved arc showing the reflex turn on the outside, which leads them to mislabel a reflex angle as acute or obtuse.
In practice, tasks using the Classify the angle template present an angle marked with an arc or give a measurement in degrees. Children compare the angle against key reference points—such as a 90° quarter-turn or a 180° straight line—to choose the correct angle type.
Children calculate unknown angles using known facts, such as angles on a straight line totalling 180° and angles around a point totalling 360°.
KS3.GM.10 apply the properties of angles at a point, angles at a point on a straight line, vertically opposite anglesKS3.GM.11 understand and use the relationship between parallel lines and alternate and corresponding anglesY5.GPS.5 use the properties of rectangles to deduce related facts and find missing lengths and anglesY6.GPS.5 recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.Y5.GPS.4.a angles at a point and one whole turn (total 360°)Y5.GPS.4.b angles at a point on a straight line and ½ a turn (total 180°)
In Year 5, children learn to calculate unknown angles by using established angle facts instead of measuring with a protractor. They find missing values using the rules that angles on a straight line (a half turn) total 180° and angles meeting at a point (a full turn) total 360°, alongside using the right angles inside rectangles.
A frequent error is mixing up the total benchmarks, such as subtracting from 360° instead of 180° for an angle on a straight line. Children also make calculation mistakes when an angle is divided into three or more parts, often subtracting only one known angle from the total and forgetting to include the others.
Tasks based on the Find the missing part of an angle template present clear geometric diagrams showing an angle split into sections, with one part marked as unknown. Children add the given degree measurements together and subtract from 180° or 360° to determine the missing value.
