Question

Heron’s formula: Area = square root 5(5-a)(5-b)(5-c) What is the area of triangle DFG? Round to the nearest whole square unit. 27 square units 38 square units 364 square units 728 square units

Answer 1

To do this problem, you will need to know the side lengths of the triangle. If you have those, just plug them in for a, b, and c and evaluate the square root.

Here is an example. If the sides are 3, 4, 5.
It would be:

$A= \sqrt{6(6-3)(6-4)(6-5))}$

The 6 is in the formula because it is the semi-perimeter (half).

Answer 2

The formula of Heron is given by:
$\sqrt{S(s-a)(s-b)(s-c)}$=A where s is given by (a+b+c)/2 and A is the area. Here, we have a=11, b=9, c=6. Hence, s=13. Substituting, we get that
A=$\sqrt{13*7*4*2}$. Thus A^2=728 and A=26.98. This yields that A=27 given the exercise options.