Heron’s Formula (Area of Triangle) MCQs Quiz | Class 9
This quiz covers Class IX Mathematics (Code 041), Unit V: Mensuration, specifically focusing on Heron’s Formula (Area of Triangle). The questions test your ability to apply Heron’s formula to solve numerical problems related to finding the area of triangles without proof. After completing the 10 MCQs, submit your answers to see your score and download a detailed PDF answer sheet for revision.
Overview of Heron’s Formula
Heron’s Formula is a fundamental concept in geometry used to determine the area of a triangle when the lengths of all three sides are known. It is particularly useful when the height of the triangle is not given, making standard area formulas difficult to apply. Named after Hero of Alexandria, this formula relates the area to the semi-perimeter of the triangle.
For a triangle with side lengths a, b, and c, the semi-perimeter s is calculated as half of the total perimeter.
Key Steps to Calculate Area
Follow these steps to find the area of any triangle using Heron’s Formula:
- Identify the lengths of the three sides: a, b, and c.
- Calculate the semi-perimeter s using the formula: s = (a + b + c) / 2.
- Substitute the values into Heron’s Formula: Area = square root of [s(s – a)(s – b)(s – c)].
- Simplify the expression to find the final area value in square units.
Formula Reference Table
| Term | Formula / Value |
|---|---|
| Perimeter (P) | a + b + c |
| Semi-perimeter (s) | (a + b + c) / 2 |
| Area of Triangle | root[ s(s-a)(s-b)(s-c) ] |
| Equilateral Triangle Area | (root 3 / 4) * side sq |
Quick Revision Points
- The formula is applicable to all types of triangles: scalene, isosceles, and equilateral.
- Ensure all side lengths are in the same unit before calculation.
- The result is always in square units (e.g., cm sq, m sq).
- If the perimeter is given along with two sides, subtract the sum of the two sides from the perimeter to find the third side first.
Extra Practice Questions
- Q1: Find the area of a triangle with sides 13 cm, 14 cm, and 15 cm. (Answer: 84 cm sq)
- Q2: Calculate the semi-perimeter of a triangle with sides 10 m, 20 m, and 24 m. (Answer: 27 m)
- Q3: Find the area of an isosceles triangle with equal sides 10 cm and base 12 cm. (Answer: 48 cm sq)
- Q4: If the perimeter of an equilateral triangle is 60 cm, find its area. (Answer: 100 root 3 cm sq)
- Q5: The sides of a triangular plot are in ratio 3:5:7 and perimeter is 300 m. Find its area. (Answer: 1500 root 3 m sq)
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