Question

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 240 b = 133 c = 174 6582.82 No triangle is formed. 11,317.51 6568.72

Answer 1

The area is 11317.51

Explanation:

The sum of 2 sides must be less than the third side (largest side) for a triangle to be formed.

b+c<a

133+174 < 240

A triangle can be formed

To use Herons formula for the area

We find S = 1/2( a+b+c)

= 1/2(240+133+174)

= 1/2 (547)

= 273.5

Area = sqrt( S (S-a) (S-b)(S-c))

sqrt((273.5 ) (273.5 -240) (273.5-133) (273.5-174))

sqrt((273.5)(33.5) (140.5) (99.5))

sqrt(128085964.4)

11317.50699

The area is 11317.51