Chapter 10: Heron’s Formula — Online MCQ Test
MATHS · CLASS 9th · Karnataka State Board
Practice Chapter 10: 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: Heron’s Formula — Important Questions & Answers
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)].
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.
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.
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.
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?
- A. 48 cm\u00b2
- B. 72 cm\u00b2
- C. 96 cm\u00b2
- D. 144 cm\u00b2
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.
When all sides of a triangle are doubled, the area becomes four times. So the new area is 4 \u00d7 24 = 96 cm\u00b2.