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How many triangles #6

(13 votes, average: 3.38 out of 5)

January 19, 2013 by puzzler 4 Comments

1.) How many triangles are there in this pentagon?

how many triangles in this pentagon

how many triangles in this pentagon

See AnswerHide Answer

There are a total of 35 triangles

How?
Lets count the number of triangles where side of the pentagon is one of the side of the triangle, for each one such side there are 6 triangles. but two of triangle has other side of the pentagon, those will be counted twice so we will count only one triangle for each side, so for five sides, total 5*5 = 25 such triangles.

Now, lets count the triangles where side of the pentagon is not the side of the triangle: there are 5+5 = 10 such triangles, this will be clear by the below diagram(5 green and 5 red triangles).

how many triangles in this pentagon answer

how many triangles in this pentagon answer

Thus, there are a total of 25+ 10= 35 triangles

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Comments

  1. Man Of Games says

    August 31, 2016 at 6:28 pm

    35

    Reply
  2. Bob says

    October 18, 2014 at 5:34 am

    84

    Reply
  3. rhea says

    June 20, 2014 at 12:45 pm

    35

    Reply
  4. BOB says

    March 6, 2013 at 6:03 pm

    I got to 30…

    Reply

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