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Gyaan Maths
CBSE · Class 6-10
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CBSE Maths · Class 9

Chapter 10: Heron's Formula

Name: ________________________
Date: ______________
Marks: ____ / 10

Formula to compute the area of a triangle when all three sides are known.

Questions

  1. Sides 7,24,257, 24, 25: area.
  2. Equilateral side 66: area.
  3. Semi-perimeter of 6,8,106, 8, 10.
  4. Sides 8,15,178, 15, 17: area.
  5. Verify Heron's formula for 6,8,106, 8, 10.
  6. Area of equilateral triangle side 1010.
  7. Sides 9,12,159, 12, 15: area.
  8. Isosceles 10,10,1210, 10, 12: area.
  9. Sides 13,14,1513, 14, 15: area.
  10. Area of a triangular park with sides 50,65,6550, 65, 65 m.

Extra Practice (Optional)

  • Area of 5,12,135, 12, 13.
  • Sides in ratio 3:5:73:5:7, perimeter 3030: area.
  • Area of quadrilateral with diagonal.
  • Equilateral triangle inscribed in a circle of radius rr: side.
  • Triangle with two equal sides 1313 and base 1010.

Answer Key (For Teachers)

  1. Answer: 8484.
    Working: s=28s = 28.
  2. Answer: 939\sqrt 3.
    Working: 34a2\tfrac{\sqrt 3}{4}a^2.
  3. Answer: 1212.
    Working: Sum /2/2.
  4. Answer: 6060.
    Working: Right triangle: 12⋅8⋅15\tfrac{1}{2}\cdot 8\cdot 15.
  5. Answer: 2424.
    Working: s=12s = 12; 12⋅6⋅4⋅2\sqrt{12\cdot 6\cdot 4\cdot 2}.
  6. Answer: 25325\sqrt 3.
    Working: 34⋅100\tfrac{\sqrt 3}{4}\cdot 100.
  7. Answer: 5454.
    Working: s=18s = 18; 2916=54\sqrt{2916} = 54.
  8. Answer: 4848.
    Working: s=16s = 16; product 23042304.
  9. Answer: 8484.
    Working: s=21s = 21; product 70567056.
  10. Answer: 15001500 m2^2.
    Working: s=90s = 90; 90⋅40⋅25⋅25\sqrt{90\cdot 40\cdot 25\cdot 25}; =2250000= \sqrt{2250000}.
Gyaan Maths · CBSE Class 9 · Chapter 10
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026