📐 Measurement Master + Algebra Lab ✨
Practise Class 8 Mensuration and Algebraic Identities with perimeter, area, surface area, volume and identity-based calculations.
📐 Class 8 Mensuration & Algebraic Identities Worksheet
50 Questions🔐 Complete Answer Key
The complete answer key stays locked until the test is completed. Individual answers appear only after checking that question.
Mensuration and Identities in One Variable for Class 8 Online Practice Worksheet
Class 8 Mensuration and Algebraic Identities Worksheet Free Online: Improve Class 8 Mathematics skills with DigiSadhan's interactive Mensuration and Algebraic Identities Online Practice Worksheet. This free tool gives students fresh practice on perimeter, area, circumference, surface area, volume and important algebraic identities. Generate up to 1,000 questions for homework, revision, tuition, classroom practice and exam preparation. Choose Foundation, Class 8 Core, Challenge or Mixed difficulty and select a topic such as Perimeter, Area, Surface Area, Volume, Algebraic Identities or Identity Value. Each question has an answer textbox and a Check Answer button. Correct answers turn green and play a positive sound and animation; incorrect answers turn red and play a retry sound and animation. Show Answer is locked until the question has been checked, encouraging students to attempt the problem independently. The full answer key remains locked until the test is completed. A live score, checked counter and progress bar help learners track their performance. Select No Timer or a 5, 10, 15, 30 or 60-minute test. The generated worksheet can be downloaded as a printable PDF. The interface is designed mobile-first for smartphones and remains responsive on tablets and desktops. Student-friendly geometry graphics make measurement concepts easier to visualise. Use this free Class 8 Maths practice resource for CBSE-style preparation, school assignments, revision, tutoring and independent learning.
Complete Class 8 Mensuration and Identities Practice Guide
What Is Mensuration?
Mensuration is the branch of mathematics concerned with measuring geometric figures. In Class 8, students work with quantities such as perimeter, area, surface area and volume. A reliable method is to identify the shape, write its formula, substitute the measurements with their units, calculate carefully and check whether the final unit is appropriate.
Perimeter of Common Figures
The perimeter of a rectangle is twice the sum of its length and breadth. For a square, all four sides are equal. When finding the perimeter of a polygon, add every side exactly once. Perimeter is measured in linear units such as cm, m or km.
Area
Area measures the surface enclosed by a two-dimensional figure and is expressed in square units. For a rectangle, multiply length by breadth. For a square, multiply its side by itself. Students should not confuse area with perimeter because they measure different quantities.
Triangle and Parallelogram
Circle
For a circle, the radius is the distance from the centre to the circumference. The diameter is twice the radius. Use the value of π specified by the question, commonly 22/7 or 3.14 at school level. Circumference is a length, while area is a square-unit measurement.
Surface Area of a Cuboid
Surface area measures the total area of all outer faces of a solid. A cuboid has three pairs of equal rectangular faces. Add the areas of all six faces to obtain the total surface area.
Surface Area of a Cube
A cube has six equal square faces. If the edge is measured in centimetres, its total surface area is in square centimetres.
Volume
Volume measures the space occupied by a three-dimensional object. It is expressed in cubic units. For a cuboid, multiply length, breadth and height. For a cube, multiply the edge three times.
Algebraic Identities
An identity is an equality that remains true for every permitted value of the variables. Identities help students expand expressions quickly and simplify calculations. The most important Class 8 identities are:
Using Identities for Quick Calculation
Identities are useful when a number is close to a convenient value. For example, 49² can be written as (50 − 1)². Then use a² − 2ab + b² to calculate 2500 − 100 + 1 = 2401. Choosing a nearby round number often makes mental calculation easier.
How to Solve Mensuration Problems
- Identify the exact figure.
- Write the required formula.
- Check whether dimensions use compatible units.
- Substitute values with units.
- Calculate in an organised order.
- Write the correct final unit.
- Check whether the answer is reasonable.
How to Solve Identity Questions
- Look for the identity pattern.
- Identify a and b.
- Write the formula before substituting.
- Expand carefully, especially the middle term 2ab.
- Combine like terms if necessary.
- Check the result by substituting a simple value.
Common Mistakes to Avoid
- Using area when the question asks for perimeter.
- Forgetting square units for area and cubic units for volume.
- Using diameter as radius in a circle formula.
- Forgetting the factor ½ in triangle area.
- Mixing centimetres and metres without conversion.
- Forgetting the middle term 2ab in square identities.
- Using a² − b² for (a − b)².
- Dropping negative signs during substitution.
Quick Revision Formula Sheet
Regular practice builds both speed and accuracy. Start with Foundation questions to reinforce formulas, use Core mode for standard Class 8 problems and use Challenge mode when you are comfortable with multi-step calculations. Shuffle the worksheet to create fresh numerical combinations. When an answer is marked wrong, check the formula, units, substitution and arithmetic instead of immediately revealing the answer. For identities, write the pattern first. For mensuration, sketch the figure when necessary. This approach helps students understand why a formula works rather than simply memorising it.