UPSC Civil Services 2018 Prelims General Studies Paper II

For easily count the number of triangles in the given three-dimensional figure, devide the given figure into three parts-top, bottom and middle.
In each of the top and bottom part, there are 5 triangles which are based on a pentagon. In middle part, there are 5 quadrilaterals inclosed between two pentagons.
Further each quadrilateral is divided into two triangles.
Hence in the middle part, there are 10 triangles.
∴ Total number of triangles in the given 3D-figure.
= (No. of triangles in top part) + (No. of triangle in bottom part) + (No. of triangle in middle part)
= 5+ 5 + 10 = 20