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

See 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).