The value of NP is 6
The Midpoint Theorem asserts that in a triangle, a line segment joining the midpoints of two sides is parallel to the third side and is half its length.
This theorem reveals a relationship between midpoints and parallel lines within a triangle.
Since SQR is formed by joining the mid point of triangle NOP, then
SR = NQ = QO
NQ = 4cm
NS = SP = SQ
SQ = 3
NS = 3
SP = 3
NP = SP + NS
= 3+3 = 6
Therefore the value of NP is 6