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Heron's Formula Practice Questions

Class 9 · Mathematics · 1473 free MCQs with instant results and detailed explanations.

1473
Total
512
Easy
723
Medium
238
Hard

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Topics in Heron's Formula

Applications 670
Area of Triangle Using Heron's Formula 803

Sample Questions from Heron's Formula

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
Using Heron's formula, what is the area of a triangle with sides 8 cm, 15 cm, and 17 cm?
A. 60 cm²
B. 68 cm²
C. 72 cm²
D. 77 cm²
Show Answer & Explanation
Correct Answer: A
The semi-perimeter is 20 cm and the area is calculated using Heron's formula as √(20(20-8)(20-15)(20-17)) = 60 cm².
Q2
Easy
If one side of a triangle is 10 cm and the other two sides are equal, what is the maximum length of the equal sides if the area must be 24 cm²?
A. 12 cm
B. 10 cm
C. 8 cm
D. 6 cm
Show Answer & Explanation
Correct Answer: C
To find the equal sides, we use Heron's formula and iterate possible values, where maximum length is found to be 8 cm.
Q3
Easy
Which of the following triangles can use Heron's formula?
A. Scalene triangle
B. Isosceles triangle
C. Equilateral triangle
D. All of the above
Show Answer & Explanation
Correct Answer: D
Heron's formula is applicable to any triangle, whether scalene, isosceles, or equilateral.
Q4
Medium
A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. What is the area of this triangle?
A. 30 cm²
B. 35 cm²
C. 36 cm²
D. 31 cm²
Show Answer & Explanation
Correct Answer: A
The triangle is a right triangle. Area = (1/2) * base * height = (1/2) * 5 * 12 = 30 cm².
Q5
Medium
Find the area of a triangle with sides 9 m, 12 m, and 15 m.
A. 54 m²
B. 60 m²
C. 72 m²
D. 66 m²
Show Answer & Explanation
Correct Answer: A
Using Heron’s formula: s = (9+12+15)/2 = 18. Area = √[18(18-9)(18-12)(18-15)] = 54 m².
Q6
Medium
If a triangle has an area of 84 m² and a base of 14 m, what is the corresponding height?
A. 12 m
B. 10 m
C. 14 m
D. 8 m
Show Answer & Explanation
Correct Answer: A
Using Area = (1/2) * base * height, height = (2 * 84) / 14 = 12 m.
Q7
Medium
A triangle has a base of 8 cm and a height of 6 cm. What is its area?
A. 24 cm²
B. 30 cm²
C. 18 cm²
D. 20 cm²
Show Answer & Explanation
Correct Answer: A
Area = (1/2) * base * height = (1/2) * 8 * 6 = 24 cm².
Q8
Hard
A triangle has sides of lengths 13 cm, 14 cm, and 15 cm. What is its area using Heron's formula?
A. 84 cm²
B. 90 cm²
C. 96 cm²
D. 72 cm²
Show Answer & Explanation
Correct Answer: A
Using Heron's formula: s = (13 + 14 + 15) / 2 = 21. Area = √[s(s-a)(s-b)(s-c)] = √[21(21-13)(21-14)(21-15)] = 84 cm².
Q9
Hard
A triangle has an area of 60 cm² and two sides measuring 8 cm and 10 cm. What could be the length of the third side?
A. 5 cm
B. 7 cm
C. 12 cm
D. 15 cm
Show Answer & Explanation
Correct Answer: B
Using Heron's formula for area, we find the possible third side must satisfy the area condition. The lengths must adhere to triangle inequality.
Q10
Hard
A triangle has two sides measuring 6 cm and 8 cm, and the area is 24 cm². What could be the length of the third side?
A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm
Show Answer & Explanation
Correct Answer: B
Use Heron's formula to check which value satisfies the area condition given the two other sides.

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Heron's Formula — Class 9 Mathematics Practice Questions Online

This page contains 1473 practice MCQs for the chapter Heron's Formula in Class 9 Mathematics. The questions are organized by difficulty — 512 easy, 723 medium, 238 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 2 topics, giving you comprehensive coverage of the entire chapter.