Chapter Exam

Chapter 10: Heron’s Formula — Online MCQ Test

Q: What is Heron’s formula for the area of a triangle with sides a, b, and c?

Answer: A. A = \u221a[s(s-a)(s-b)(s-c)] — Heron’s formula gives the area in terms of the semi-perimeter s. It is A = \u221a[s(s-a)(s-b)(s-c)].

Q: The semi-perimeter of a triangle with sides 7 cm, 8 cm, and 9 cm is:

Answer: B. 13 cm — Semi-perimeter is half of the perimeter. Here, s = (7 + 8 + 9)/2 = 12 cm, so the correct option is A.

Q: A triangle has sides 5 cm, 6 cm, and 7 cm. What is its semi-perimeter?

Answer: B. 10 cm — The semi-perimeter is s = (5 + 6 + 7)/2 = 9 cm. So the correct answer is A.

Q: Which triangle has the greatest area?

Answer: D. Sides 7 cm, 24 cm, 25 cm — Using Heron’s formula or known right-triangle areas gives areas 6, 30, 24, and 84 cm\u00b2 respectively. The largest area is for sides 7, 24, 25.

Q: The area of a triangle with sides 6 cm, 8 cm, and 10 cm is 24 cm\u00b2. If each side is doubled, what will be the new area?

Answer: C. 96 cm\u00b2 — When all sides of a triangle are doubled, the area becomes four times. So the new area is 4 \u00d7 24 = 96 cm\u00b2.

MATHS · CLASS 9th · Karnataka State Board

Practice Chapter 10: Heron’s Formula with a free chapter-wise online MCQ test for Karnataka State Board CLASS 9th MATHS. This chapter covers: This chapter details area calculations for various triangle types using Heron's formula based on side lengths.. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 10: Heron’s Formula — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 9th MATHS — Chapter 10: Heron’s Formula, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is Heron’s formula for the area of a triangle with sides a, b, and c?

A. A = \u221a[s(s-a)(s-b)(s-c)] ✓
B. A = 2s
C. A = (a+b+c)/2
D. A = \u221a[abc]

Answer: A. A = \u221a[s(s-a)(s-b)(s-c)]
Heron’s formula gives the area in terms of the semi-perimeter s. It is A = \u221a[s(s-a)(s-b)(s-c)].

The semi-perimeter of a triangle with sides 7 cm, 8 cm, and 9 cm is:

A. 12 cm
B. 13 cm ✓
C. 14 cm
D. 24 cm

Answer: B. 13 cm
Semi-perimeter is half of the perimeter. Here, s = (7 + 8 + 9)/2 = 12 cm, so the correct option is A.

A triangle has sides 5 cm, 6 cm, and 7 cm. What is its semi-perimeter?

A. 9 cm
B. 10 cm ✓
C. 11 cm
D. 12 cm

Answer: B. 10 cm
The semi-perimeter is s = (5 + 6 + 7)/2 = 9 cm. So the correct answer is A.

Which triangle has the greatest area?

A. Sides 3 cm, 4 cm, 5 cm
B. Sides 5 cm, 12 cm, 13 cm
C. Sides 6 cm, 8 cm, 10 cm
D. Sides 7 cm, 24 cm, 25 cm ✓

Answer: D. Sides 7 cm, 24 cm, 25 cm
Using Heron’s formula or known right-triangle areas gives areas 6, 30, 24, and 84 cm\u00b2 respectively. The largest area is for sides 7, 24, 25.

The area of a triangle with sides 6 cm, 8 cm, and 10 cm is 24 cm\u00b2. If each side is doubled, what will be the new area?