Mensuration 2D Notes for SSC Exams

Mensuration 2D is about the area and perimeter of flat shapes. Two to four questions come from mensuration (2D and 3D together) in each SSC Tier 1 paper, and the formulas are asked directly. These mensuration 2D notes for SSC give you all plane figure formulas in one table, with solved examples and practice questions.

Area and Perimeter Formulas

Heron's Formula and Special Triangle Results

• Heron's formula: Area = square root of s(s - a)(s - b)(s - c), where s = (a + b + c)/2.
• Diagonal of a square = side x root 2.
• Diagonal of a rectangle = square root of (l squared + b squared).
• Height of an equilateral triangle = (root 3 / 2) x side.
• Area of a triangle = r x s, where r is the inradius and s is the semi-perimeter.
• Pythagorean triplets: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25).

Circle and Related Figures

• Take pi = 22/7 when the radius is a multiple of 7, otherwise use 3.14.
• Area of a ring (annulus) = pi (R squared - r squared).
• Length of an arc = (theta / 360) x 2 pi r. Area of a sector = (theta / 360) x pi r squared.
• If the radius becomes n times, the area becomes n squared times.

Changes in Dimensions

If the length and breadth of a rectangle are increased by x% and y%, the area changes by x + y + xy/100 percent. If the side of a square increases by 10%, its area increases by 10 + 10 + 1 = 21%.

Solved Examples

Example 1: Find the area and perimeter of a rectangle of length 12 cm and breadth 8 cm.
Solution: Area = 12 x 8 = 96 square cm. Perimeter = 2(12 + 8) = 40 cm.

Example 2: The diagonal of a square is 10 cm. Find its area.
Solution: Area = d squared / 2 = 100 / 2 = 50 square cm.

Example 3: Find the area of a triangle with sides 13 cm, 14 cm and 15 cm.
Solution: s = 21. Area = square root of (21 x 8 x 7 x 6) = square root of 7056 = 84 square cm.

Example 4: Find the area and circumference of a circle of radius 7 cm.
Solution: Area = 22/7 x 49 = 154 square cm. Circumference = 2 x 22/7 x 7 = 44 cm.

Example 5: The parallel sides of a trapezium are 10 cm and 14 cm and the distance between them is 6 cm. Find its area.
Solution: Area = 1/2 x (10 + 14) x 6 = 72 square cm.

Example 6: The diagonals of a rhombus are 16 cm and 12 cm. Find its area and side.
Solution: Area = 1/2 x 16 x 12 = 96 square cm. Side = square root of (8 squared + 6 squared) = 10 cm.

Quick Tips to Solve Faster

• Memorise the Pythagorean triplets to find sides without calculation.
• Use the diagonal formulas for squares and rectangles directly.
• Use 22/7 for pi whenever the radius or diameter is a multiple of 7.
• Convert all dimensions into the same unit before calculating.
• For percentage change in area, use x + y + xy/100.

Common Mistakes to Avoid

• Using the slant side instead of the height in the area of a triangle or parallelogram.
• Mixing the area formula with the perimeter formula.
• Using diameter in place of radius for a circle.
• Not squaring the unit while converting area from metres to centimetres.
• Forgetting the 1/2 in the triangle and trapezium formulas.

Quick Revision Points

• Rectangle: area = lb, perimeter = 2(l + b).
• Triangle: area = 1/2 x base x height; Heron's formula for three sides.
• Circle: area = pi r squared and circumference = 2 pi r.
• Rhombus area = 1/2 x d1 x d2.
• Pythagorean triplets: 3-4-5, 5-12-13, 8-15-17, 7-24-25.

Practice Questions With Answers

1. Find the area of a rectangle of length 15 cm and breadth 6 cm.
   Answer: 90 square cm (15 x 6).
2. Find the perimeter of a square of area 144 square cm.
   Answer: 48 cm (Side = 12).
3. Find the area of a triangle with base 10 cm and height 8 cm.
   Answer: 40 square cm (1/2 x 10 x 8).
4. Find the area of a circle of diameter 14 cm.
   Answer: 154 square cm (22/7 x 7 x 7).
5. Find the area of an equilateral triangle of side 6 cm.
   Answer: 9 root 3 square cm ((root 3 / 4) x 36).
6. Find the area of a parallelogram of base 12 cm and height 5 cm.
   Answer: 60 square cm (12 x 5).
7. Find the side of a rhombus with diagonals 10 cm and 24 cm.
   Answer: 13 cm (Square root of (25 + 144)).
8. Find the perimeter of a semicircle of radius 7 cm.
   Answer: 36 cm (22 + 14).
9. The perimeter of a rectangle is 56 cm and its length is 20 cm. Find its breadth.
   Answer: 8 cm (28 - 20).
10. Find the circumference of a circular track of radius 21 m.
    Answer: 132 m (2 x 22/7 x 21).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC mensuration practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Mensuration 3D Notes
• Triangle Geometry Notes
• Circle Geometry Notes
• Square Root and Cube Root Notes
• SSC Mensuration Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is mensuration?

Mensuration is the branch of maths that deals with the measurement of length, area and volume of figures.

What is the difference between area and perimeter?

Perimeter is the total length of the boundary, while area is the space covered inside the shape.

What is Heron's formula?

Area of a triangle = square root of s(s - a)(s - b)(s - c), where s is half the perimeter.

What value of pi should I use?

Use 22/7 when the radius is a multiple of 7, and 3.14 or the given value in other cases.

How many questions come from mensuration in SSC exams?

Two to four questions come from mensuration (2D and 3D together) in SSC Tier 1.

What is the area of a rhombus?

Area of a rhombus = 1/2 x product of its diagonals.

What is the effect on area when the radius is doubled?

The area becomes four times because the area depends on the square of the radius.

How should I practise mensuration?

Memorise the table, solve the examples here and attempt the mensuration practice paper.