Chapter 12 Revision Quiz: Heron's Formula & Area Concepts
Welcome to the Class 9 Chapter 12 Chapter-End Quiz! This practice set contains high-yield MCQs modeled after previous year questions (PYQs) from competitive exams such as SSC GD, RRB NTPC, and Class 9 Board Revision. Test your speed, concept clarity, and problem-solving skills.
Question 1
The sides of a triangular field are 13 cm, 14 cm, and 15 cm. Find the area of the triangle using Heron's formula.
- A) 42 cm²
- B) 84 cm²
- C) 168 cm²
- D) 96 cm²
View Solution
Correct Answer: B) 84 cm²
Step-by-step Solution:
1. Calculate semi-perimeter s = (a + b + c) / 2 = (13 + 14 + 15) / 2 = 42 / 2 = 21 cm.
2. Using Heron's formula: Area = √[s(s - a)(s - b)(s - c)]
Area = √[21 × (21 - 13) × (21 - 14) × (21 - 15)]
Area = √[21 × 8 × 7 × 6]
Area = √[(7 × 3) × (4 × 2) × 7 × (3 × 2)]
Area = √(7² × 3² × 4²)
Area = 7 × 3 × 4 = 84 cm².
Question 2
An isosceles triangle has a perimeter of 30 cm and each of its equal sides is 12 cm. Find the area of the triangle.
- A) 9√15 cm²
- B) 6√15 cm²
- C) 12√15 cm²
- D) 15√15 cm²
View Solution
Correct Answer: A) 9√15 cm²
Step-by-step Solution:
1. Equal sides a = 12 cm, b = 12 cm.
2. Third side c = Perimeter - (a + b) = 30 - 24 = 6 cm.
3. Semi-perimeter s = 30 / 2 = 15 cm.
4. Area = √[15 × (15 - 12) × (15 - 12) × (15 - 6)]
Area = √[15 × 3 × 3 × 9]
Area = √(15 × 9 × 9) = 9√15 cm².
Question 3 (SSC GD PYQ)
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area.
- A) 1500 m²
- B) 3000 m²
- C) 1500√3 m²
- D) 750√3 m²
View Solution
Correct Answer: C) 1500√3 m²
Step-by-step Solution:
1. Let the sides be 3x, 5x, and 7x.
2. Perimeter = 3x + 5x + 7x = 15x = 300 m ⇒ x = 20 m.
3. Sides are a = 60 m, b = 100 m, c = 140 m.
4. Semi-perimeter s = 300 / 2 = 150 m.
5. Area = √[150 × (150 - 60) × (150 - 100) × (150 - 140)]
Area = √[150 × 90 × 50 × 10] = √67500000 = 1500√3 m².
Question 4 (RRB NTPC PYQ)
The area of an equilateral triangle is 16√3 cm². Find its perimeter.
- A) 12 cm
- B) 24 cm
- C) 36 cm
- D) 18 cm
View Solution
Correct Answer: B) 24 cm
Step-by-step Solution:
1. Area of equilateral triangle = (√3 / 4) × side².
2. (√3 / 4) × a² = 16√3 ⇒ a² = 16 × 4 = 64 ⇒ a = 8 cm.
3. Perimeter = 3 × side = 3 × 8 = 24 cm.
Question 5
The edges of a triangular board are 6 cm, 8 cm, and 10 cm. Find the cost of painting it at the rate of 90 paise per cm².
- A) ₹ 21.60
- B) ₹ 43.20
- C) ₹ 24.00
- D) ₹ 18.50
View Solution
Correct Answer: A) ₹ 21.60
Step-by-step Solution:
1. Observe that 6² + 8² = 36 + 64 = 100 = 10², so it is a right-angled triangle.
2. Area = (1/2) × base × height = (1/2) × 6 × 8 = 24 cm².
3. Rate = ₹ 0.90 per cm².
4. Total cost = 24 × 0.90 = ₹ 21.60.
Excellent work on solving these Class 9 Chapter 12 competitive math questions! Master these Heron's Formula short-cuts and formula variations to score full marks in school exams as well as competitive tests like RRB and SSC GD.
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