Chapter Exam

Chapter 10 MATHS : Heron's Formula — Online MCQ Test

Q: What is the formula for the semi-perimeter (s) of a triangle with sides a, b, and c?

Answer: A. s = (a + b + c) / 2 — The semi-perimeter is defined as half of the perimeter of the triangle.

Q: Heron's formula for the area of a triangle is given by:

Answer: A. Area = sqrt(s(s-a)(s-b)(s-c)) — Heron's formula states that Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.

Q: Find the area of an equilateral triangle with side 'a'.

Answer: B. (sqrt(3) / 4) * a² — Using Heron's formula for s=3a/2, the area simplifies to (sqrt(3)/4)a².

Q: Which of the following sets of side lengths CANNOT form a triangle?

Answer: C. 1, 2, 3 — The sum of any two sides must be greater than the third side. Here, 1+2 is not > 3.

Q: The percentage increase in the area of a triangle if each side is increased by 100% is:

Answer: C. 300% — Increasing each side by 100% means new sides are 2x original. New area = 4 * old area. Increase = (4A - A)/A * 100 = 300%.

MATHS · CLASS 9th · Andhra State Board

Practice Chapter 10 MATHS : Heron's Formula with a free chapter-wise online MCQ test for Andhra 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 MATHS : Heron's Formula — Important Questions & Answers (FAQ)

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

What is the formula for the semi-perimeter (s) of a triangle with sides a, b, and c?

A. s = (a + b + c) / 2 ✓
B. s = a + b + c
C. s = (a + b + c) / 3
D. s = 2(a + b + c)

Answer: A. s = (a + b + c) / 2
The semi-perimeter is defined as half of the perimeter of the triangle.

Heron's formula for the area of a triangle is given by:

A. Area = sqrt(s(s-a)(s-b)(s-c)) ✓
B. Area = s(s-a)(s-b)(s-c)
C. Area = sqrt(s+a+b+c)
D. Area = 1/2 * base * height

Answer: A. Area = sqrt(s(s-a)(s-b)(s-c))
Heron's formula states that Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.

Find the area of an equilateral triangle with side 'a'.

A. sqrt(3) * a²
B. (sqrt(3) / 4) * a² ✓
C. (sqrt(3) / 2) * a²
D. 1/2 * a²

Answer: B. (sqrt(3) / 4) * a²
Using Heron's formula for s=3a/2, the area simplifies to (sqrt(3)/4)a².

Which of the following sets of side lengths CANNOT form a triangle?

A. 2, 3, 4
B. 3, 4, 5
C. 1, 2, 3 ✓
D. 5, 5, 8

Answer: C. 1, 2, 3
The sum of any two sides must be greater than the third side. Here, 1+2 is not > 3.

The percentage increase in the area of a triangle if each side is increased by 100% is:

A. 100%
B. 200%
C. 300% ✓
D. 400%

Answer: C. 300%
Increasing each side by 100% means new sides are 2x original. New area = 4 * old area. Increase = (4A - A)/A * 100 = 300%.

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