Is right triangle or not

If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.

Result

A =  54.415

Solution:

a=13 b=11.5 c=22.5  c1=a2+b2=132+11.52≐17.3566 c1<>c  s=a+b+c2=13+11.5+22.52=472=23.5  A=s⋅ (s−a)⋅ (s−b)⋅ (s−c)=23.5⋅ (23.5−13)⋅ (23.5−11.5)⋅ (23.5−22.5)≐3 329≐54.4151≐54.415a=13 \ \\ b=11.5 \ \\ c=22.5 \ \\ \ \\ c_{1}=\sqrt{ a^2+b^2 }=\sqrt{ 13^2+11.5^2 } \doteq 17.3566 \ \\ c_{1}<>c \ \\ \ \\ s=\dfrac{ a+b+c }{ 2 }=\dfrac{ 13+11.5+22.5 }{ 2 }=\dfrac{ 47 }{ 2 }=23.5 \ \\ \ \\ A=\sqrt{ s \cdot \ (s-a) \cdot \ (s-b) \cdot \ (s-c) }=\sqrt{ 23.5 \cdot \ (23.5-13) \cdot \ (23.5-11.5) \cdot \ (23.5-22.5) } \doteq 3 \ \sqrt{ 329 } \doteq 54.4151 \doteq 54.415

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Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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