What is the area of a triangle with sides of 14, 17, and 12 ?

Since you were given all three sides, you can use Heron's formula to find the area.

Heron's formula: A = square root[ s * (s - a) * (s - b) * (s - c) ] where a, b, and c are sides of the triangle and s is the semiperimeter (a + b +c) / 2

 

Let's solve for s first:

s = (14 + 17 + 12) / 2

s = 43 / 2

s = 21. 5

Now plug in the values into Heron's formula:

A = square root [ 21.5 * (21.5 - 14) * (21.5 - 17) * (21.5 - 12) ]

A = square root [ 21.5 * (7.5) * (4.5) * (9.5) ]

A = square root [6893.4375]

A ≈ 83.067

A ≈ 83