The sides of triangle $XYZ$ are $13\text{ cm}$, $14\text{ cm}$ and $15\text{ cm}$. Find its area (in cm${}^2$).

Step-by-step solution

1. Compute the semiperimeter: $s=\frac{13+14+15}{2}=\frac{42}{2}=21\text{ cm}$.
2. Apply Heron's formula: $\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}$, where $a=13$, $b=14$, $c=15$.
3. Calculate each factor: $s-a=21-13=8$, $s-b=21-14=7$, $s-c=21-15=6$.
4. Multiply: $s(s-a)(s-b)(s-c)=21\times 8\times 7\times 6$.
5. Simplify: $21\times 8=168$, $7\times 6=42$, then $168\times 42=7056$.
6. Take the square root: $\sqrt{7056}=84$.
7. Thus the area of the triangle is $84{\text{ cm}}^2$.

Concept tested: Heron's formula for area

Published 21 August 2026 · How this solution was prepared and checked

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