Imaginesis: printable Year 6 Measurement maths worksheets for England (National Curriculum) — Finding the Perimeter of a Rectangle, Finding the Volume of Cubes and Cuboids, Finding the Area and Missing Sides of a Rectangle: word problems with hints, answers and worked solutions as PDF, also as a test in groups A–D.
Luca checks a rectangular sprout mat in the garden that is 4 centimetres wide and 7 centimetres high. What is the distance all the way around the mat in centimetres?
Hint: A rectangle has two sides of 4 centimetres and two sides of 7 centimetres. Add the lengths of all four sides of the sprout mat together to find the distance around it.
Answer: 22
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
A triangular flower bed has one side 13 m long, and its height to that side, measured at a right angle, is 4 m. How many square metres does the flower bed cover?
Hint: Imagine a rectangle with the same side and the same height around the flower bed. What part of that rectangle does the flower bed fill?
Answer: 26 m²
Children calculate and draw perimeters of rectangles in centimetres and metres, find missing side lengths, and compare perimeters across different shapes.
Y3.M.2 measure the perimeter of simple 2-D shapesY4.M.2 measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metresY6.M.4 recognise that shapes with the same areas can have different perimeters and vice versa
In Year 6, children calculate the total boundary around rectangles using measurements in centimetres and metres. Building on earlier measurement of flat shapes, they work flexibly with rectangle dimensions: adding all four sides, using given measurements to find unknown side lengths, and exploring how different shapes compare in perimeter.
A frequent mistake happens when children add only the two labelled sides—length and width—and forget to account for the opposite two sides, resulting in half the actual perimeter. Children also commonly confuse perimeter with area, multiplying length by width rather than adding the lengths of all four outer edges together.
Worksheet tasks present rectangles with labelled dimensions or placed on a grid. Children solve questions such as finding the missing side of a rectangle when the perimeter is provided, determining which figure has the greater perimeter, verifying if a given perimeter calculation is correct, or using a ruler to draw a rectangle with the given perimeter.
Children learn to calculate and compare the volume of cubes and cuboids using standard cubic units such as cm³ and m³, moving from unit blocks to multiplication.
KS3.GM.1 derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)Y5.M.5 estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]Y6.M.7 calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³].
In Year 6, children learn to calculate, estimate, and compare the volume of cubes and cuboids. Working with standard units such as cubic centimetres (cm³) and cubic metres (m³)—and extending to units like mm³—they build on earlier practical work with 1 cm³ blocks to determine total volume by multiplying length, width, and height.
A common error occurs when children add the three dimensions together rather than multiplying them, or confuse volume with surface area by finding and adding the areas of the outer faces. Children also frequently mix up units, writing square measurements like cm² instead of cubic units like cm³.
Tasks begin with finding the volume from unit cubes, where children count visible blocks or calculate layers. They then advance to finding the volume of a rectangular prism with labelled side measurements, and finally solve composite problems requiring them to find the volume of a solid made of two joined prisms by splitting the shape into two separate cuboids.
Children learn to calculate rectangle areas using standard units and find unknown side lengths using division when the area is already known.
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 6, children apply the formula for the area of a rectangle (multiplying length by width) using standard units such as square centimetres (cm²) and square metres (m²). They also work in reverse: using properties of rectangles and inverse operations, they divide the total area by a known side length to deduce the missing side.
A frequent mistake occurs when finding an unknown dimension: children often subtract the known side from the total area instead of dividing, confusing the multiplicative relationship of area with additive measures. Another common confusion is mixing up area and perimeter, mistakenly adding the outer lengths when asked to find the surface space inside.
Worksheet tasks draw from three concrete formats: straightforward calculations in Area of a rectangle, algebraic reasoning where the area and one dimension are provided in Missing side of a rectangle, and practical word problems in Area of a rectangle in everyday life involving real-world surfaces like garden patches or floors.
Children learn to calculate the area of a triangle by multiplying the base by the perpendicular height and dividing the product by two.
KS3.GM.1 derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)Y6.M.6 calculate the area of parallelograms and triangles
In Year 6, children learn to calculate the area of different types of triangles. Building on their understanding of rectangles and parallelograms, they identify the base and the vertical height, multiply these two dimensions together, and divide by two to find the total area.
A common error occurs when children use the length of a slanted side instead of the true perpendicular height, particularly in isosceles, equilateral, or obtuse triangles. Another frequent slip is simply multiplying the base and height together but forgetting the final step of halving the result.
Worksheet activities based on the Area of a triangle template present drawings of triangles with labelled measurements. Children must select the correct base and perpendicular height—ignoring any extra side lengths provided—and calculate the area in square units.
