Heron’s formula – Triangle with sides 13 cm, 14 cm, 15 cm: Find the exact area (in square centimetres) of a triangle whose side lengths are 13 cm, 14 cm, and 15 cm.

Introduction / Context:For a triangle given by three sides, use Heron’s formula: Area = √(s(s − a)(s − b)(s − c)), where s is the semiperimeter.

Given Data / Assumptions:

• a = 13 cm, b = 14 cm, c = 15 cm.
• All sides satisfy the triangle inequality.

Concept / Approach:Compute s, then apply Heron’s formula carefully without rounding until the end to keep it exact.

Step-by-Step Solution:

Verification / Alternative check:13-14-15 is a classic Heron triple yielding area 84; many exam keys list this as a standard exact value.

Why Other Options Are Wrong:64, 44, 22 are not consistent with Heron’s calculation for these sides.

Common Pitfalls:Arithmetic slips in semiperimeter or inside the square root; premature rounding.

Final Answer:84