Herons Formula Quiz: Calculate Area with Herons Formula

  • 10th Grade
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Attempts: 13 | Questions: 20 | Updated: Dec 17, 2025
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1) Find the area of a triangle with sides 3 cm, 4 cm, and 5 cm.

Explanation

s = (3+4+5)/2 = 6. A = √[6(6–3)(6–4)(6–5)] = √[6×3×2×1] = √36 = 6 cm².

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About This Quiz
Herons Formula Quiz: Calculate Area With Herons Formula - Quiz

How can you compute a triangle’s area using only its side lengths? In this quiz, you’ll explore Heron’s formula and learn how to apply it efficiently to triangles of all shapes. You’ll practice calculating semi-perimeters, organizing steps carefully, and working through examples where traditional height-based formulas are inconvenient. Through guided... see moreproblems, you’ll develop confidence using Heron’s method and deepen your understanding of how side lengths alone can determine a triangle’s exact area.
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2) A triangle has sides 5 m, 6 m, and 7 m. Find its area.

Explanation

s = (5+6+7)/2 = 9. A = √[9(9–5)(9–6)(9–7)] = √[9×4×3×2] = √216 = 14.70 m².

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3) Heron’s formula can be used for any triangle when all three sides are known.

Explanation

True. Heron’s formula applies to all types of triangles, as long as the three sides are known.

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4) Find the area of a triangle with sides 7 cm, 8 cm, and 9 cm.

Explanation

s = (7+8+9)/2 = 12. A = √[12(12–7)(12–8)(12–9)] = √[12×5×4×3] = √720 = 26.83 cm².

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5) Find the area when sides are 6 m, 8 m, and 10 m.

Explanation

s = (6+8+10)/2 = 12. A = √[12(12–6)(12–8)(12–10)] = √[12×6×4×2] = √576 = 24 m².

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6) Heron’s formula gives the same result as base×height÷2 when applied to right triangles.

Explanation

True. For right triangles, Heron’s formula simplifies to ½ × base × height.

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7) Find the area if sides are 13 cm, 14 cm, and 15 cm.

Explanation

s = (13+14+15)/2 = 21. A = √[21(21–13)(21–14)(21–15)] = √[21×8×7×6] = √7056 = 84 cm².

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8) A triangle has sides 8 m, 15 m, and 17 m. Find its area.

Explanation

s = (8+15+17)/2 = 20. A = √[20(20–8)(20–15)(20–17)] = √[20×12×5×3] = √3600 = 60 m².

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9) Select all correct forms of Heron’s formula.

Explanation

The correct formulas are s = (a+b+c)/2 and A = √[s(s–a)(s–b)(s–c)].

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10) Find the area of a triangle with sides 9 cm, 10 cm, and 17 cm.

Explanation

s = (9+10+17)/2 = 18. A = √[18(18–9)(18–10)(18–17)] = √[18×9×8×1] = √1296 = 36 cm².

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11) The semi-perimeter is always half of the triangle’s perimeter.

Explanation

True. By definition, s = (a+b+c)/2, which is half the perimeter.

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12) Find the area if sides are 10 m, 14 m, and 18 m.

Explanation

s = (10+14+18)/2 = 21. A = √[21(21–10)(21–14)(21–18)] = √[21×11×7×3] = √4851 = 69.65 ≈ 69.6 m².

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13) Find the area if sides are 5 cm, 12 cm, and 13 cm.

Explanation

s = (5+12+13)/2 = 15. A = √[15(15–5)(15–12)(15–13)] = √[15×10×3×2] = √900 = 30 cm².

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14) All side lengths must satisfy the triangle inequality for Heron’s formula to work.

Explanation

True. The sum of any two sides must be greater than the third for a valid triangle.

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15) Find the area of a triangle with sides 7 m, 24 m, and 25 m.

Explanation

s = (7+24+25)/2 = 28. A = √[28(28–7)(28–24)(28–25)] = √[28×21×4×3] = √7056 = 84 m².

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16) Select all statements true about Heron’s formula.

Explanation

Heron’s formula needs only side lengths, works for any triangle, and does not require height or angles.

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17) Find the area of a triangle with sides 9 m, 10 m, and 11 m.

Explanation

s = (9+10+11)/2 = 15. A = √[15(15–9)(15–10)(15–11)] = √[15×6×5×4] = √1800 = 42.43 m².

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18) Find the area of a triangle with sides 14 cm, 15 cm, and 13 cm.

Explanation

s = (14+15+13)/2 = 21. A = √[21(21–14)(21–15)(21–13)] = √[21×7×6×8] = √7056 = 84 cm².

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19) The semi-perimeter (s) of a triangle is given by s = ______.

Explanation

Semi-perimeter s = (a + b + c)/2 is half the sum of all sides.

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20) The formula for finding the area using Heron’s formula is A = ______.

Explanation

Area of a triangle with sides a, b, and c is A = √[s(s–a)(s–b)(s–c)].

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Find the area of a triangle with sides 3 cm, 4 cm, and 5 cm.
A triangle has sides 5 m, 6 m, and 7 m. Find its area.
Heron’s formula can be used for any triangle when all three sides...
Find the area of a triangle with sides 7 cm, 8 cm, and 9 cm.
Find the area when sides are 6 m, 8 m, and 10 m.
Heron’s formula gives the same result as base×height÷2 when...
Find the area if sides are 13 cm, 14 cm, and 15 cm.
A triangle has sides 8 m, 15 m, and 17 m. Find its area.
Select all correct forms of Heron’s formula.
Find the area of a triangle with sides 9 cm, 10 cm, and 17 cm.
The semi-perimeter is always half of the triangle’s perimeter.
Find the area if sides are 10 m, 14 m, and 18 m.
Find the area if sides are 5 cm, 12 cm, and 13 cm.
All side lengths must satisfy the triangle inequality for Heron’s...
Find the area of a triangle with sides 7 m, 24 m, and 25 m.
Select all statements true about Heron’s formula.
Find the area of a triangle with sides 9 m, 10 m, and 11 m.
Find the area of a triangle with sides 14 cm, 15 cm, and 13 cm.
The semi-perimeter (s) of a triangle is given by s = ______.
The formula for finding the area using Heron’s formula is A =...
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