Heron’s Formula Practice Problems with Answers

There are six (6) practice problems here about Heron’s Formula. The more problems you solve, the more proficient you get. Please enjoy!

For your convenience, here’s the formula.

Heron's Formula to find the area of triangle with sides a, b, and c.

PRACTICE PROBLEMS

Note: drawings not to scale

Problem 1: Find the area of the triangle below using Heron’s formula.

triangle SRQ has sides 11 km, 7 km, and 5 km
Answer
area of triangle SRQ is 13 square kilometers

Therefore, the area of [latex]\triangle{SRQ}[/latex] is about [latex]13[/latex] square kilometers.

Problem 2: Find the area of the triangle below using Heron’s formula.

triangle ABC has sides 12 cm, 9 cm, and 13 cm
Answer
area of triangle ABC equals 52 square centimeters

Therefore, the area of [latex]\triangle{ABC}[/latex] is about [latex]52[/latex] square centimeters.

Problem 3: Find the area of the triangle below using Heron’s formula.

triangle PRQ has sides 12 yards, 7 yards, and 15 yards
Answer
area of triangle PRQ is 41 square yards

Therefore, the area of [latex]\triangle{PRQ}[/latex] is about [latex]41[/latex] square yards.

Problem 4: Find the area of the triangle below using Heron’s formula.

triangle XYZ has sides 6 inches, 15 inches, and 12 inches
Answer
area of triangle XYZ is 34 square inches

Therefore, the area of [latex]\triangle{XYZ}[/latex] is about [latex]34[/latex] square inches.

Problem 5: Find the area of the triangle below using Heron’s formula.

triangle JKL has sides 13 feet, 14 feet, and 10 feet
Answer
area of triangle JKL is 62 square feet

Therefore, the area of [latex]\triangle{JKL}[/latex] is about [latex]62[/latex] square feet.

Problem 6: Find the area of the triangle below using Heron’s formula.

triangle VUT has sides 5 feet, 13 feet, and 11 feet
Answer
area of triangle VUT is 27 square feet

Therefore, the area of [latex]\triangle{VUT}[/latex] is about [latex]27[/latex] square feet.

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Heron’s Formula