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 yards, of ΔABC.

Answer 1

Answer:

The area of ΔABC is 6√6 sq. yards.

Step-by-step explanation:

The area of a triangle using the Heron's formula is:

$A=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}$

Here s is given as follows:

$s=\frac{a+b+c}{2}$

The sides of the triangle ABC are as follows:

AB = 6 yd

BC = 7 yd

CA = 5 yd

Compute the value of s as follows:

$s=\frac{a+b+c}{2}$

  $=\frac{6+7+5}{2}\\\\=9$

Compute the area of ΔABC as follows:

$A=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}$

   $=\sqrt{9\cdot(9-6)\cdot(9-7)\cdot(9-5)}\\\\=\sqrt{9\times 3\times 2\times 4}\\\\=\sqrt{216}\\\\=\sqrt{36\times 6}\\\\=6\sqrt{6}$

Thus, the area of ΔABC is 6√6 sq. yards.