Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Value Based Questions- Heron’s Formula
Class 9 Maths Chapter 10 Question Answers - Heron’s Formula
Question 1. Sarika participated in a drawing competition. She is required to make a design on a rectangular sheet of dimensions 50 cm × 70 cm. In the design she made 8 triangles, each of sides 26 cm, 17 cm and 25 cm as shown in the figure.
(i) Find the total area of the design.
(ii) Find the remaining area of the sheet.
(iii) By drawing a design in a competition, which value is depicted by Sarika?
Solution. (i) Sides of a triangle are: a = 26 cm, b = 17 cm and c = 25 cm
Using, Hero’s formula,
= 2 × 17 × 2 × 3 cm2 = 204 cm2
∵ The design is having 8 equal (congruent) triangles.
∴ Total area of the design = 8 × (Area of one triangle) = 8 × 204 cm2
= 1632 cm2
(ii) Total area of the sheet =70 cm × 50 cm = 3500 cm2
∴ Remaining area of the sheet = (3500 – 1632) cm2
= 1868 cm2
(iii) Creativity.
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FAQs on Class 9 Maths Chapter 10 Question Answers - Heron’s Formula
| 1. What is Heron's formula and how is it used to find the area of a triangle? |  |
Ans. Heron's formula is a mathematical formula used to find the area of a triangle when the lengths of its sides are known. It is given by the formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle and a, b, and c are the lengths of its sides.
| 2. Why is Heron's formula important in geometry? | |
Ans. Heron's formula is important in geometry because it provides a method to calculate the area of a triangle without needing to know its height or base. This formula is particularly useful when dealing with triangles that do not have a right angle.
| 3. Can Heron's formula be used for all types of triangles? | |
Ans. Yes, Heron's formula can be used for all types of triangles, whether they are equilateral, isosceles, or scalene. It is a general formula that can be applied to any triangle as long as the lengths of its sides are known.
| 4. How does Heron's formula relate to the Pythagorean theorem? | |
Ans. Heron's formula and the Pythagorean theorem are related in the sense that both are used to solve problems related to triangles. However, they serve different purposes. The Pythagorean theorem is used to find the length of one side of a right-angled triangle when the lengths of the other two sides are known. Heron's formula, on the other hand, is used to find the area of any type of triangle when the lengths of its sides are known.
| 5. Can Heron's formula be used to find the area of a quadrilateral or any other polygon? | |
Ans. No, Heron's formula is specifically designed to find the area of a triangle. It cannot be directly applied to find the area of a quadrilateral or any other polygon with more than three sides. For other polygons, different formulas or methods need to be used to find their areas.
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