Chapter 10 MATHS : Heron's Formula — Online MCQ Test
MATHS · CLASS 9th · Andhra State Board
Practice Chapter 10 MATHS : Heron's Formula with a free chapter-wise online MCQ test.
This chapter covers: This chapter details area calculations for various triangle types using Heron's formula based on side lengths..
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Chapter 10 MATHS : Heron's Formula — Important Questions & Answers
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.
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.
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.
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 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%.
Increasing each side by 100% means new sides are 2x original. New area = 4 * old area. Increase = (4A - A)/A * 100 = 300%.