Question

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square meters, of ΔABC.

a=7m, b=5m, c=6m

Answer 1

Answer: S=6√6 m².

Explanation:

Heron's formula

`\displaystyle\\\boxed {S=√(p*(p-a)(p-b)(p-c)) }`,

a, b, c - sides of a triangle,

`\displaystyle\\p=(a+b+c)/(2)`

S - triangle area.

a=7 m, b=5 m, c=6 m.

`p=(7+5+6)/(2) \\p=(18)/(2) \\p=9 (m).`

Hence,

`S=√(9*(9-7)*(9-5)*(9-6))\\S=3*√(2*4*3)\\S=3*2*√(2*3) \\S=6√(6) \ (m^2).`