The area of triangle DEF having sides 3, 5, 6 is 2[tex]\sqrt{14}[/tex]square units
What is Heron's formula?
Heron's formula, formula credited to Heron for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides: Area = Square root √ s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.
How to calculate area of triangle?
The semi perimeter is calculated=(3+5+6)/2
=7
To calculate the area of DEF we have to put s=7, a=3, b=5, c=6. So,
Area of DEF=[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
=7(7-3)(7-5)(7-6)
=7*4*2*1
=[tex]\sqrt{56}[/tex]
=2[tex]\sqrt14}[/tex] square units.
Hence the area of DEF is 56 square units.
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