2D Figures (Perimeter & Area)
SSC GD Exam Preparation - Quantitative Aptitude
This chapter covers 2D (Two-Dimensional) figures that have length and breadth only, no height. We'll calculate their Perimeter (boundary length) and Area (surface covered).
🔹 1. Square
Formulas:
Perimeter = 4a
Area = a²
Example:
Side = 6 cm
Perimeter = 4 × 6 = 24 cm
Area = 6² = 36 cm²
🔹 2. Rectangle
Formulas:
Perimeter = 2(L + B)
Area = L × B
Example:
Length = 10 cm, Breadth = 6 cm
Perimeter = 2(10 + 6) = 32 cm
Area = 10 × 6 = 60 cm²
🔹 3. Triangle
Formulas:
Perimeter = a + b + c
Area (right triangle) = ½ × base × height
Heron's Formula: s = (a+b+c)/2
Area = √[s(s-a)(s-b)(s-c)]
Example:
Base = 8 cm, Height = 5 cm
Area = ½ × 8 × 5 = 20 cm²
🔹 4. Parallelogram
Formulas:
Area = base × height
Perimeter = 2(a + b)
Example:
Base = 10 cm, Height = 4 cm
Area = 10 × 4 = 40 cm²
🔹 5. Rhombus
All sides equal.
Formulas:
Perimeter = 4a
Area = (d₁ × d₂)/2
🔹 6. Trapezium (Trapezoid)
Formula:
Area = ½ × (a + b) × h
(a, b = parallel sides)
🔹 7. Circle
Formulas:
Circumference = 2πr
Area = πr²
Use π = 22/7 or 3.14
🔹 8. Semi-Circle
Radius = r
Formulas:
Perimeter = πr + 2r
Area = ½πr²
🔹 9. Ring / Annulus
Outer radius = R, Inner radius = r
Area Formula:
Area = π(R² - r²)
🧠 Practice Section: 15 Questions (With Answers)
Each Q followed by its Answer (SSC style). Click on "View Answer" to check your understanding.
Q1. Find the perimeter of a square of side 9 cm.
View Answer
Perimeter = 4 × 9 = 36 cm
Q2. Find area of square of side 12 cm.
View Answer
Area = 12² = 144 cm²
Q3. Length = 15 m, Breadth = 5 m. Find area.
View Answer
Area = 15 × 5 = 75 m²
Q4. Find perimeter of rectangle: L=18 cm, B=7 cm.
View Answer
Perimeter = 2(18 + 7) = 50 cm
Q5. Base of a triangle = 10 cm, height = 6 cm. Find area.
View Answer
Area = ½ × 10 × 6 = 30 cm²
Q6. Circle radius = 7 cm. Find circumference.
View Answer
Circumference = 2πr = 2 × 22/7 × 7 = 44 cm
Q7. Circle radius = 7 cm. Find area.
View Answer
Area = πr² = 22/7 × 49 = 154 cm²
Q8. Parallelogram: base = 12 cm, height = 8 cm. Find area.
View Answer
Area = 12 × 8 = 96 cm²
Q9. Rhombus diagonals = 10 cm and 24 cm. Find area.
View Answer
Area = (10 × 24)/2 = 120 cm²
Q10. Trapezium parallel sides = 8 cm, 12 cm, height = 5 cm.
View Answer
Area = ½(8 + 12) × 5 = 50 cm²
Q11. Semi-circle radius = 14 cm. Find area.
View Answer
Area = ½πr² = ½ × 22/7 × 196 = 308 cm²
Q12. Semi-circle radius = 14 cm. Find perimeter.
View Answer
Perimeter = πr + 2r = 44 + 28 = 72 cm
Q13. Find area of ring: R=10 cm, r=7 cm.
View Answer
Area = π(100 − 49) = 51π ≈ 160.22 cm²
Q14. Rectangular field 40 m × 25 m. Find perimeter.
View Answer
Perimeter = 2(40 + 25) = 130 m
Q15. Triangle sides = 7, 8, 9. Find area (Heron).
View Answer
s = (7+8+9)/2 = 12
Area = √[12×5×4×3] = √720 ≈ 26.83 cm²
✅ SSC GD Exam Strategy
🟢 Memorize key formulas for different 2D shapes
🟢 Practice unit conversions (cm to m, etc.)
🟢 Master Heron's formula for triangles with all sides
🟢 Understand the difference between perimeter and area
🟢 Time yourself - aim for 30-45 seconds per mensuration question
You've completed 2D Mensuration!
SSC GD Tip: Mastering 2D mensuration is essential for solving geometry problems efficiently. Remember that perimeter is the total length around a shape, while area is the space it covers. Practice identifying which formula to use for different shapes. For complex shapes, break them down into simpler ones. Regular practice with previous year SSC GD questions will build your speed and accuracy in solving these problems. Pay special attention to circle and triangle problems as they frequently appear in exams.
Master 2D Mensuration for SSC GD Exam!
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