In square ABCD,P and Q are mid points of AB and CD resp.If AB=8cm and PQ and BD intersect at O,then find the area of triangle OPB.

 

P and Q are mid points of AB and CD respectively.

So, PQ is parallel to AC.

=> OP is parallel to AC.

Hence, OP = 1/2 AC = 1/2 * 8 = 4 cm   [Side of square is given as 8 cm]

 

ar(triangle OPB) = 1/2 * PB * OP = 1/2 * 4 cm * 4 cm = 8 cm²