triangle

Geometry Level 1

If the sides of a triangular field are 37 m, 684 m and 685 m, then its area is


The answer is 12654.

Ram Gautam by Ram Gautam , 22, India

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3 solutions

Drop TheProblem
Sep 4, 2014

It's simply a right-angled triangle (37^2+684^2=685). So area=37*684/2=12654.

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Gerardo Lozada
Aug 28, 2014

Cosine law: 37^2 = 684^2 + 685^2 - 2 684 685 cos(theta), theta = 3.096315394 degrees. Triangle height = 684 sin(theta) = 36.945985356 m. Triangle area = (1/2) base height = (1/2) 685 36.945985356 = 12,654 sq. m.

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@Gerardo Lozada No need to complicate solutions like that(in this case). The solution provided by @Drop TheProblem is good(for solving problems like these)

Anuj Shikarkhane - 6 years, 7 months ago
Ram Gautam
Aug 24, 2014

We find the semi-perimeter of the triangle,

37+684+685/2= 718

By Using Heron's formula, we get,

Sqr rt[ s(s-a)(s-b)(s-c)]

And after a lot of solving you'll finally get the answer! :-)

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