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CBSE Class 9 Mathematics Question 3 of 6

Heron's Formula — Question 3

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Question 3

There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour. NCERT Class 9 Mathematics CBSE Solutions.
Answer

Let a, b and c be the sides of the triangle.

Let a = 11 m, b = 6 m and c = 15 m.

By formula,

Semi Perimeter (s) = Perimeter of triangle2=a+b+c2\dfrac{\text{Perimeter of triangle}}{2} = \dfrac{a + b + c}{2}

= 11+6+152=322\dfrac{11 + 6 + 15}{2} = \dfrac{32}{2} = 16 m.

By Heron's formula,

Area of triangle (A) = s(s−a)(s−b)(s−c)\sqrt{s(s - a)(s - b)(s - c)} sq.units

Substituting values we get :

A=16(16−11)(16−6)(16−15)=16×5×10×1=800=202 m2.A = \sqrt{16(16 - 11)(16 - 6)(16 - 15)} \\[1em] = \sqrt{16 \times 5 \times 10 \times 1} \\[1em] = \sqrt{800} \\[1em] = 20\sqrt{2} \text{ m}^2.

Hence, area of the wall painted in colour = 20220\sqrt{2} m2.

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Mathematics | Heron's FormulaWeb Content • Interactive Notes

Heron’s Formula — Interactive Study Guide

The Formula

s = (a+b+c)/2
Area = √[s(s−a)(s−b)(s−c)]

Works for ANY triangle. No need to know the height!

Step-by-Step Calculation

Sides: 5, 12, 13

s = (5+12+13)/2 = 15

s−5 = 10, s−12 = 3, s−13 = 2

Area = √(15×10×3×2) = √900 = 30 sq units

Verify: This is a right triangle (5²+12²=13²), so area = ½×5×12 = 30. Matches!

Quick Self-Check

  1. Find area of equilateral Δ with side 6. (s=9, A=√(9×3×3×3)=9√3)
  2. Find area of triangle with sides 3, 4, 5. (6 sq units)

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