Circles & Quadrilaterals
SSC GD Exam Preparation - Quantitative Aptitude
Geometry questions on Circles and Quadrilaterals are common in competitive exams. Focus is on basic properties, formulas, and problem-solving.
🔹 1. Circles
Key Terms:
Radius (r)
Distance from center to any point on the circle
Diameter (d)
Twice the radius, d = 2r
Circumference (C)
Distance around the circle, C = 2πr
Area (A)
Space inside circle, A = πr²
Special Segments & Angles:
Chord
Line joining two points on a circle
Tangent
Line touching circle at one point (perpendicular to radius)
Arc
Part of circle between two points
Sector Area
(θ/360) × πr², θ in degrees
Key Formulas:
Circumference = 2πr
Area = πr²
Diameter = 2r
Sector Area = (θ/360) × πr²
🔹 2. Quadrilaterals
1. Square
All sides equal, all angles 90°
Area = a²
Perimeter = 4a
2. Rectangle
Opposite sides equal, all angles 90°
Area = l × b
Perimeter = 2(l + b)
3. Parallelogram
Opposite sides equal & parallel
Area = b × h
Perimeter = 2(a + b)
4. Rhombus
All sides equal, opposite angles equal
Area = ½ × d₁ × d₂
5. Trapezium
One pair of opposite sides parallel
Area = ½ × (a + b) × h
6. Kite
Two pairs of adjacent sides equal
Area = ½ × d₁ × d₂
🧠 Practice Section: 15 Questions (With Answers)
Each Q followed by its Answer (SSC style). Click on "View Answer" to check your understanding.
Q1. Find circumference of a circle with radius 7 cm
View Answer
C = 2πr = 2 × 22/7 × 7 = 44 cm
Q2. Area of a circle with radius 5 cm
View Answer
A = πr² = 22/7 × 5² = 78.57 cm²
Q3. Diameter of a circle with radius 9 cm
View Answer
d = 2r = 18 cm
Q4. Length of tangent from a point on radius of 12 cm
View Answer
Tangent = radius at point → forms 90°, use Pythagoras for any triangle if required
Q5. Area of sector with radius 7 cm and angle 90°
View Answer
A = (90/360) × π × 7² = ¼ × 154 = 38.5 cm²
Q6. Area of a square with side 8 cm
View Answer
A = a² = 8² = 64 cm²
Q7. Perimeter of rectangle with length 10 cm and breadth 5 cm
View Answer
P = 2(l + b) = 2(10 + 5) = 30 cm
Q8. Area of parallelogram with base 12 cm and height 5 cm
View Answer
A = b × h = 12 × 5 = 60 cm²
Q9. Area of rhombus with diagonals 10 cm and 12 cm
View Answer
A = ½ × d₁ × d₂ = ½ × 10 × 12 = 60 cm²
Q10. Area of trapezium with parallel sides 10 cm, 6 cm, height 5 cm
View Answer
A = ½(a + b)h = ½(10 + 6) × 5 = 40 cm²
Q11. Perimeter of kite with sides 5 cm and 7 cm
View Answer
P = 2(a + b) = 2(5 + 7) = 24 cm
Q12. Angle sum of any quadrilateral
View Answer
360°
Q13. If a square has side 6 cm, find perimeter
View Answer
P = 4a = 4 × 6 = 24 cm
Q14. Find radius of circle if area = 154 cm² (π=22/7)
View Answer
A = πr² ⇒ r² = 154 × 7 / 22 = 49 ⇒ r = 7 cm
Q15. A rectangle has area 60 cm², length 12 cm. Find breadth
View Answer
b = A/l = 60/12 = 5 cm
✅ SSC GD Exam Strategy
🟢 Memorize all circle formulas (circumference, area, diameter)
🟢 Practice quadrilateral area and perimeter calculations
🟢 Master sector area calculations
🟢 Learn to identify different quadrilateral types quickly
🟢 Time yourself - aim for 25-40 seconds per geometry problem
You've completed Geometry: Circles & Quadrilaterals!
SSC GD Tip: Mastering circle and quadrilateral properties is crucial for solving geometry problems efficiently. Remember the key formulas for circumference, area, and sector calculations. For quadrilaterals, focus on identifying the type and applying the correct area formula. Regular practice with previous year SSC GD questions will build your speed and accuracy. Pay special attention to circle problems involving radius, diameter, and circumference as they frequently appear in exams. Understanding the relationship between different quadrilateral types will help you solve problems faster.
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