Class 9 Math: Heron's Formula Important Exam Questions
Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 9 Heron's Formula to help you test your mastery.
Exam-Pattern Questions and Answers
Question 1 (HARD)
This is a descriptive problem. Work out all steps on paper before checking the solution.
Solution Explanation & Steps: Perimeter of triangular field = 120 + 80 + 60 = 260 m (i) Length of wire needed for single fencing = 260 - 30 (to be left for gate on each side) = 230 m Total length of wire needed for double fencing = 2 × 230 = 460 m (ii) Cost of fencing = 6 per metre Total cost of fencing = 460 × 6 = 2760 (iii) Given a = 120 m, b = 80 m and c = 60 m The semi-perimeter, s = 260 2 = 130 m Using Heron’s formula, Area of triangular field ( )( )( ) 130(130 120)(130 80)(130 60)s s a s b s c= - - - = - - - 2130 10 50 70 100 455 100 21.33 2133 m= × × × = = × = OR Anurag makes a kite using red and yellow piece of paper. Red piece of paper is cut in the shape of square with diagonal 30 cm. At one of the vertex of this square, a yellow paper with the shape of an equilateral triangle of side such that a2 = 32√3 is attached to give the shape of a kite. Find the total area of paper required to make the kite. Ans. Let ABCD be the square made by red piece of paper. Diagonal AC and BD bisect each other at right angle. The area of square ABCD in terms of diagonal is given by ar(ABCD) = 1 2 × BD2 = 1 2 × (30)2 = 900 2 = 450 cm2 Red paper area = 450 cm2 Area of equilateral ΔCEF is given by ar(ΔCEF) = 3 4 × a2 = 3 4 × 32 3 (Given a2 = 32 3 ) = 8 × 3 = 24 cm2 Yellow paper area = 24 cm2 Total area of paper required to make the kite = Red paper area + Yellow paper area = 450 + 24 = 474 cm2
Question 2 (EASY)
- Option 1: Systematic application of coordinate rules
- Option 2: Advanced integral equations
- Option 3: Infinite boundary coordinates
- Option 4: None of the above
Solution Explanation & Steps: Studying Area of triangle by Heron's formula requires mastering basic coordinate relationships first.
Question 3 (MEDIUM)
- Option 1: The dependent variable
- Option 2: The constant offset
- Option 3: The complex exponent
- Option 4: The vertical coordinate
Solution Explanation & Steps: To solve algebraic equations under Area of triangle by Heron's formula, we isolate the single dependent variable.
Grading Step-Marking Guidelines
Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.