Real World Herons Formula Quiz: Real World Herons Formula

  • 10th Grade
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| Questions: 20 | Updated: Dec 17, 2025
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1) A triangular plot has sides 50 ft, 75 ft, and 100 ft. Find its area.

Explanation

s = (50+75+100)/2 = 112.5. A = √[112.5(112.5–50)(112.5–75)(112.5–100)] = √[112.5×62.5×37.5×12.5] = √3,296,630.86 ≈ 1,815.46 ft².

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About This Quiz
Real World Herons Formula Quiz: Real World Herons Formula - Quiz

How does Heron’s formula apply to real-life measurement problems? In this quiz, you’ll use the formula to analyze practical geometry scenarios where triangle dimensions come from surveys, distances, or physical layouts. You’ll practice interpreting word problems, organizing given information, and computing area without needing height measurements. Each question helps you... see moresee how Heron’s formula bridges theoretical geometry with everyday applications, making complex shapes easier to understand and evaluate accurately.
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2) A garden shaped like a triangle has sides 30 m, 40 m, and 50 m. Find its area.

Explanation

s = (30+40+50)/2 = 60. A = √[60(60–30)(60–40)(60–50)] = √[60×30×20×10] = √360000 = 600 m².

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3) Heron’s formula can be used to find the area of any triangle if all three sides are known.

Explanation

True. Heron’s formula applies to any triangle with known side lengths.

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4) The semi-perimeter (s) is calculated as s = ______.

Explanation

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

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5) Find the area of a triangular park with sides 7 m, 8 m, and 9 m.

Explanation

s = (7+8+9)/2 = 12. A = √[12(12–7)(12–8)(12–9)] = √[12×5×4×3] = √720 = 26.83 m².

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6) A plot has sides 10 m, 14 m, and 18 m. Find its area.

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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7) The semi-perimeter is always greater than any one side of the triangle.

Explanation

True. s = (a+b+c)/2 is always greater than each individual side in a valid triangle.

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8) Find the area of a field with sides 9 m, 10 m, and 17 m.

Explanation

s = (9+10+17)/2 = 18. A = √[18(18–9)(18–10)(18–17)] = √[18×9×8×1] = √1296 = 36 m².

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9) A triangular lawn has sides 13 m, 14 m, and 15 m. Find its area.

Explanation

s = (13+14+15)/2 = 21. A = √[21(21–13)(21–14)(21–15)] = √[21×8×7×6] = √7056 = 84 m².

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10) Select all correct formulas related to Heron’s formula.

Explanation

Heron’s formula: A = √[s(s–a)(s–b)(s–c)], where s = (a+b+c)/2.

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11) A triangle has sides 9 m, 15 m, and 18 m. Find its area.

Explanation

s = (9+15+18)/2 = 21. A = √[21(21–9)(21–15)(21–18)] = √[21×12×6×3] = √4536 = 67.35 m².

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12) Heron’s formula works for equilateral, isosceles, and scalene triangles.

Explanation

True. It applies to all triangles, regardless of type.

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13) The area of a triangle using Heron’s formula is A = ______.

Explanation

Area = √[s(s–a)(s–b)(s–c)], where s = (a+b+c)/2.

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14) A triangular plot has sides 15 m, 20 m, and 25 m. Find its area.

Explanation

s = (15+20+25)/2 = 30. A = √[30(30–15)(30–20)(30–25)] = √[30×15×10×5] = √22500 = 150 m².

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15) A triangular garden has sides 6 m, 8 m, and 10 m. Find its area.

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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16) If one side of a triangle is longer than the sum of the other two sides, Heron’s formula cannot be used.

Explanation

True. That would violate the triangle inequality, and such a triangle cannot exist.

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17) Find the area of a triangular land 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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18) Select all statements that are true about Heron’s formula.

Explanation

Heron’s formula uses side lengths and semi-perimeter and applies to all triangle types.

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19) 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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20) Find the area of a triangle with sides 14 m, 15 m, and 13 m.

Explanation

s = (14+15+13)/2 = 21. A = √[21(21–14)(21–15)(21–13)] = √[21×7×6×8] = √7056 = 84 m².

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A triangular plot has sides 50 ft, 75 ft, and 100 ft. Find its area.
A garden shaped like a triangle has sides 30 m, 40 m, and 50 m. Find...
Heron’s formula can be used to find the area of any triangle if all...
The semi-perimeter (s) is calculated as s = ______.
Find the area of a triangular park with sides 7 m, 8 m, and 9 m.
A plot has sides 10 m, 14 m, and 18 m. Find its area.
The semi-perimeter is always greater than any one side of the...
Find the area of a field with sides 9 m, 10 m, and 17 m.
A triangular lawn has sides 13 m, 14 m, and 15 m. Find its area.
Select all correct formulas related to Heron’s formula.
A triangle has sides 9 m, 15 m, and 18 m. Find its area.
Heron’s formula works for equilateral, isosceles, and scalene...
The area of a triangle using Heron’s formula is A = ______.
A triangular plot has sides 15 m, 20 m, and 25 m. Find its area.
A triangular garden has sides 6 m, 8 m, and 10 m. Find its area.
If one side of a triangle is longer than the sum of the other two...
Find the area of a triangular land with sides 7 m, 24 m, and 25 m.
Select all statements that are 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 m, 15 m, and 13 m.
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