Geometry
Class 9

Heron's Formula

A=s(sa)(sb)(sc),s=a+b+c2A = \sqrt{s(s-a)(s-b)(s-c)}, \quad s = \frac{a+b+c}{2}
5101502468101214
A = √[s(s-a)(s-b)(s-c)], s = (a+b+c)/2

Adjust Variables

Side a
a =
120
Side b
b =
120

Triangle area from three sides. s is semi-perimeter. Works when height is unknown or hard to find.

Real-World Applications

Land surveying — Irregular plot areas from boundary measurements.

Construction — Triangular roof sections.

Architecture — Triangular window and facade areas.

GPS — Trilateration area calculations.

Fabric cutting — Minimum material for triangular patches.

Sail making — Triangular sail areas.

Truss design — Triangular structural element areas.

Map calculations — Distances known, finding enclosed area.

Forestry — Triangular plot demarcation.

Archaeology — Site boundary calculations.

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