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If your Class 8 guide still has a chapter called "Mensuration" with cuboids and cylinders, it may be describing the old book. NCERT's new Class 8 mathematics textbook, Ganita Prakash, comes in two parts. Area of flat figures now has its own chapter, and surface area has moved up a year. This post shows where each idea sits, works through every formula you need with numbers, and ends with a short practice routine.
Where is mensuration in the new Class 8 NCERT book?
The older NCERT book, Mathematics for Class 8, had Chapter 9, Mensuration, as its contents page shows. The new Ganita Prakash Part II, first published in December 2025, divides the work differently:
Chapter 7, Area, covers triangles, parallelograms, rhombuses, trapeziums and the area of any polygon.
Chapter 4, Exploring Some Geometric Themes, covers visualising solids: faces, edges, vertices and nets of cubes, cuboids, cylinders and cones.
Surface area and volume appear in the new Class 9 book, as Chapter 14, "Math of Space: Surface Area and Volume", in Ganita Manjari Part II.
Schools can move between editions at different speeds, so ask your teacher which book your class follows this year.
How do you find the area of any polygon?
Chapter 7 of Ganita Prakash Part II builds on one idea: any polygon can be divided into triangles, and the area of a triangle is ½ × base × height. Every other formula in the chapter is a shortcut built on that.
Worked example 1. A quadrilateral ABCD has diagonal AC = 18 cm. The perpendicular from B to AC is 5 cm, and the perpendicular from D to AC is 7 cm.
Triangle ABC: ½ × 18 × 5 = 45 cm²
Triangle ACD: ½ × 18 × 7 = 63 cm²
Area of ABCD = 45 + 63 = 108 cm²
You could also write this as ½ × 18 × (5 + 7) = 108 cm². The diagonal is a shared base for both triangles.
What are the formulas for a parallelogram, rhombus and trapezium?
The chapter derives each one by cutting and rearranging shapes, and its summary lists:
Parallelogram: base × height
Rhombus: ½ × product of the diagonals
Trapezium: ½ × height × sum of the parallel sides
Worked example 2 (rhombus). The diagonals of a rhombus are 16 cm and 12 cm. Area = ½ × 16 × 12 = 96 cm². The diagonals of a rhombus bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs 8 cm and 6 cm. By the Baudhāyana-Pythagoras theorem (Chapter 2 of the same book), the side is √(64 + 36) = √100 = 10 cm, and the perimeter is 4 × 10 = 40 cm.
Worked example 3 (trapezium). A trapezium has parallel sides of 12 cm and 8 cm, and the distance between them is 5 cm. Area = ½ × 5 × (12 + 8) = ½ × 5 × 20 = 50 cm².
Check it another way, as the book does: two copies of this trapezium, one turned around, join into a parallelogram with base 12 + 8 = 20 cm and height 5 cm. That parallelogram has area 20 × 5 = 100 cm², and one trapezium is half of it, 50 cm².
Where does surface area fit now?
Chapter 4 asks you to draw nets: flat shapes that fold into a solid. A net already holds the idea of surface area, because the surface area of a solid is the area of its net.
Worked example 4. A closed box (a cuboid) measures 5 cm × 4 cm × 3 cm. Its net has three pairs of rectangles:
Two of 5 × 4 = 20 cm²
Two of 4 × 3 = 12 cm²
Two of 5 × 3 = 15 cm²
Total = 2 × (20 + 12 + 15) = 2 × 47 = 94 cm²
You do not need a formula in Class 8; drawing the net and adding the rectangles gives the answer. The formal treatment comes in Class 9, and our guide to surface areas and volumes in Class 9 picks it up from there.
Which mistakes cost the most marks?
Using a slanted side as the height. A parallelogram with sides 10 cm and 6 cm does not have area 60 cm² unless it is a rectangle.
Forgetting the ½. The triangle, rhombus and trapezium formulas all carry it.
Adding the wrong sides of a trapezium. Only the two parallel sides go inside the bracket.
Mixing units. 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm². Convert lengths before you multiply.
Assuming area grows like length. If you double every side of a rectangle, the area becomes four times as large, not twice. A 3 cm × 2 cm rectangle has area 6 cm²; a 6 cm × 4 cm rectangle has area 24 cm², which is 4 × 6.
The last slip is well studied. Van Dooren and colleagues (2005) note that earlier research found students over-rely on proportional methods in topics such as geometry. In their own test of 1,062 students from Grades 2 to 8, many still applied proportional methods where they did not fit, even in Grade 8.
How should you practise area this week?
Day 1: Redo the four worked examples above without looking, then check your numbers.
Day 2: For each formula, write its derivation in two lines (for example, "two trapeziums make a parallelogram").
Day 3: Draw an irregular quadrilateral or pentagon on squared paper, split it into triangles, measure, and find its area in two different ways.
Day 4: Do a mixed set: two triangles, two trapeziums, two rhombuses and two nets, shuffled so that you must choose the formula each time.
Day 5: Make up one problem of each type for a friend, and check theirs.
If you find it hard to picture how two trapeziums form a parallelogram, or how a net folds into a box, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Tonight, open out an empty matchbox or carton, measure its net, and find its surface area by adding the rectangles.
