Mensuration
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Area of Trapezium, Rhombus and Polygons
The area of a trapezium is half of the height times the sum of its two parallel sides. The area of a rhombus is half of the product of its two diagonals. For a polygon with many sides, we cut it into triangles, rectangles or trapeziums, find each area and add them.
Why it matters. Land, floors and garden plots are rarely plain rectangles. Splitting a shape into simple pieces is a skill children use in all later geometry.
Try it in two minutes
- Draw a trapezium on paper with parallel sides of 6 cm and 10 cm and a height of 4 cm. Ask for its area using half of the height times the sum of the parallel sides.
- Cut out the shape, then cut it into two triangles along a diagonal and check by adding the two triangle areas.
- Draw a rhombus with diagonals 8 cm and 6 cm and ask your child to find the area.
- Ask: how would you find the area of a house-shaped pentagon?
Try at home. Ask your child to sketch their room floor as two rectangles and add the areas.
Surface Area of Cube and Cuboid
The surface area of a solid is the total area of all its faces. A cuboid has three pairs of equal rectangular faces, so its total surface area is 2(lb + bh + hl). A cube has 6 equal square faces, so its area is 6 times edge times edge. The lateral surface area counts only the four side faces.
Why it matters. Surface area tells us how much paint, paper or cloth we need to cover a box or a room. Mixing it up with volume is a very common mistake.
Try it in two minutes
- Pick up a cereal box and measure its length, width and height with a ruler.
- Ask your child to find the area of the front and back faces together, then the sides, then the top and bottom.
- Add the three pairs to get the total surface area.
- Ask: if we only wrap the four sides with a paper strip, which area is that?
Try at home. Ask your child to estimate the area of the four walls of their room using a measuring tape.
Surface Area of a Cylinder
A cylinder such as a tin has one curved surface and two circular faces. If the curved surface is cut and opened flat, it becomes a rectangle with length 2πr and width h, so its area is 2πrh. Adding the two circles gives the total surface area 2πr(r + h).
Why it matters. Labels, paint and metal sheets for tins, pipes and tanks all depend on cylinder surface area. Children often forget the circular faces or use the volume formula by mistake.
Try it in two minutes
- Take an empty tin or a toilet-roll tube. Wrap a strip of paper around it so that it fits exactly.
- Measure the strip: its length is the circumference and its width is the height.
- Ask your child to multiply the two to find the curved area.
- Trace the top circle on paper and ask what must be added for the total area.
Try at home. Ask your child to find how much paper is needed for the label of a small tin, if they know its radius and height.
Volume of Cuboid, Cube and Cylinder
Volume is the amount of space a solid takes up. We count it in unit cubes. A cuboid has volume length times breadth times height, a cube has edge times edge times edge, and a cylinder has πr²h. All these are base area times height.
Why it matters. Volume is used to compare boxes, tanks and containers. Children often confuse volume with surface area or forget that volume is measured in cubic units.
Try it in two minutes
- Take a small box and some sugar cubes or dice. Fill the base layer and count the cubes in it.
- Count how many layers fit. Ask your child to multiply the cubes per layer by the layers.
- Measure the box and check that length times breadth times height gives the same number.
- Ask: what happens to the volume if you stack two such boxes?
Try at home. Ask your child to find the volume of a tin using its radius and height, and say the unit.
Volume and Capacity
Volume is the space an object occupies. Capacity is how much a container can hold, and it can be given in litres. We use 1 mL = 1 cm³, 1 litre = 1000 cm³ and 1 m³ = 1000 litres. To find the capacity of a box, work out its volume in cm³ and change it to litres.
Why it matters. Water tanks, bottles, buckets and fuel are measured in litres, but boxes are measured in centimetres. Children need the link between the two to solve real-life problems.
Try it in two minutes
- Take a 1 litre bottle and a small box with measurements of 10 cm each side.
- Ask your child to find the volume of the box in cm³. It is 1000 cm³.
- Fill the box with water and pour it into the bottle. Ask: how much of the litre is filled?
- Ask: what is 1 mL in cm³ and how many mL make a litre?
Try at home. Ask your child to find the capacity of a lunch box in litres from its measurements.
What your child will practise
- Area of Trapezium, Rhombus and Polygons: Number Quest (Collect the Answer)
- Surface Area of a Cylinder: Space Quick Fire (Quick Fire)
- Surface Area of Cube and Cuboid: Jungle Puzzle (Clue Puzzle)
- Volume and Capacity: Lab Explorer Sort (Sort It Out)
- Volume of Cuboid, Cube and Cylinder: Candy Quick Fire (Quick Fire)
- Quiz: Area of Trapezium, Rhombus and Polygons (8 questions)
- Quiz: Surface Area of Cube and Cuboid (8 questions)
- Quiz: Surface Area of a Cylinder (8 questions)
- Quiz: Volume and Capacity (8 questions)