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.

Step-by-step explanation:

                                   Heron's formula

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

a, b, c - sides of a triangle,

$\displaystyle\\p=\frac{a+b+c}{2}$

S - triangle area.

a=7 m,  b=5 m,  c=6 m.

$p=\frac{7+5+6}{2} \\p=\frac{18}{2} \\p=9 (m).$

Hence,

$S=\sqrt{9*(9-7)*(9-5)*(9-6)}\\S=3*\sqrt{2*4*3}\\S=3*2*\sqrt{2*3} \\S=6\sqrt{6} \ (m^2).$