Compute Triangle Areas with Heron’s Formula

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| Questions: 20 | Updated: Nov 10, 2025
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1) Find the area of a triangle with sides 3, 4, and 5.

Explanation

Right triangle ⇒ A = ½·3·4 = 6. Hence, area = 6.

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About This Quiz
Compute Triangle Areas With Herons Formula - Quiz

Build the foundation: verify side lengths form a triangle, compute the semiperimeter, and set up the product that leads to the area. You’ll decide when Heron’s Formula is the right tool, interpret units, and compare different side sets to predict which triangles enclose more area—before you even crunch the... see morenumbers. see less

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2) A triangle has sides 6 m, 8 m, and 10 m. What is its area?

Explanation

Right triangle (3–4–5 scaled by 2). Area = ½·6·8 = 24 m².

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3) For sides 5, 6, and 7, what is the semiperimeter s?

Explanation

s = (5 + 6 + 7)/2 = 9. Hence, s = 9.

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4) Using Heron’s Formula, find the area of a triangle with sides 5, 6, and 7.

Explanation

s = 9 ⇒ A = √(9·4·3·2) = √216 = 6√6 ≈ 14.7.

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5) A triangle has sides 9 m, 10 m, and 17 m. Can it exist?

Explanation

9 + 10 = 19 > 17, so valid triangle.

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6) The semiperimeter of a triangle is 12 cm, and the sides are 5, 7, and 10. What is s − a?

Explanation

Take a = 5 ⇒ s − a = 12 − 5 = 7.

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7) Find the area of a triangle with sides 8, 15, and 17.

Explanation

Right triangle ⇒ A = ½·8·15 = 60.

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8) A triangle has sides 7 m, 8 m, and 9 m. Approximate its area to one decimal place.

Explanation

s = 12 ⇒ A = √(12·5·4·3) = √720 ≈ 26.8 m².

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9) A triangle with sides 5 cm, 5 cm, and 6 cm has an area of approximately:

Explanation

s = 8 ⇒ A = √(8·3·3·2) = √144 = 12.

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10) Find the area of a triangle with sides 9 ft, 12 ft, and 15 ft.

Explanation

Right triangle ⇒ A = ½·9·12 = 54 ft².

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11) A triangle has sides 10 m, 13 m, and 15 m. Find its area.

Explanation

s = 19 ⇒ A = √(19·9·6·4) = √4104 ≈ 64.1 m² 

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12) For triangle sides 13 cm, 14 cm, and 15 cm, find the semiperimeter s.

Explanation

s = (13 + 14 + 15)/2 = 21.

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13) Using Heron’s Formula, find the area for sides 13, 14, and 15.

Explanation

s = 21 ⇒ A = √(21·8·7·6) = √7056 = 84.

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14) A triangle with sides 9 m, 10 m, and 11 m has an area of approximately:

Explanation

s = 15 ⇒ A = √(15·6·5·4) = √1800 ≈ 42.4.

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15) A triangular garden has sides 8 m, 8 m, and 10 m. What is the area?

Explanation

s = 13 ⇒ A = √(13·5·5·3) = √975 = 5√39 m².

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16) A triangular flag has sides 10 ft, 10 ft, and 12 ft. Find its area.

Explanation

s = 16 ⇒ A = √(16·6·6·4) = √2304 = 48 ft².

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17) A triangular park has sides 9 m, 9 m, and 9 m. What is the approximate area?

Explanation

Equilateral a = 9 ⇒ A = (√3/4)a² = (√3/4)·81 ≈ 35.1 m² 

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18) A triangular ramp has sides 7 ft, 24 ft, and 25 ft. Find its area.

Explanation

Right triangle ⇒ A = ½·7·24 = 84 ft².

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19) For triangle sides 6 cm, 8 cm, and 10 cm, which statement is true?

Explanation

6² + 8² = 10² ⇒ right triangle, area = 24 cm².

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20) A triangle has sides 9 m, 10 m, and 15 m. Approximate its area.

Explanation

s = 17 ⇒ A = √(17·8·7·2) = √1904 ≈ 43.6 m²

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Find the area of a triangle with sides 3, 4, and 5.
A triangle has sides 6 m, 8 m, and 10 m. What is its area?
For sides 5, 6, and 7, what is the semiperimeter s?
Using Heron’s Formula, find the area of a triangle with sides 5, 6,...
A triangle has sides 9 m, 10 m, and 17 m. Can it exist?
The semiperimeter of a triangle is 12 cm, and the sides are 5, 7, and...
Find the area of a triangle with sides 8, 15, and 17.
A triangle has sides 7 m, 8 m, and 9 m. Approximate its area to one...
A triangle with sides 5 cm, 5 cm, and 6 cm has an area of...
Find the area of a triangle with sides 9 ft, 12 ft, and 15 ft.
A triangle has sides 10 m, 13 m, and 15 m. Find its area.
For triangle sides 13 cm, 14 cm, and 15 cm, find the semiperimeter s.
Using Heron’s Formula, find the area for sides 13, 14, and 15.
A triangle with sides 9 m, 10 m, and 11 m has an area of...
A triangular garden has sides 8 m, 8 m, and 10 m. What is the area?
A triangular flag has sides 10 ft, 10 ft, and 12 ft. Find its area.
A triangular park has sides 9 m, 9 m, and 9 m. What is the approximate...
A triangular ramp has sides 7 ft, 24 ft, and 25 ft. Find its area.
For triangle sides 6 cm, 8 cm, and 10 cm, which statement is true?
A triangle has sides 9 m, 10 m, and 15 m. Approximate its area.
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