Question

In square ABCD, P and Q are the midpoints of sides AB and CD respectively. If AB = 8 cm and PQ and BD intersect at O, then find the area of $△OPB.$

Answer 1

In square ABCD, P and Q are the midpoints of sides AB and CD respectively.
PQ and BD are joined which intersect each other at O.
Side of square AB = 8 cm

$\therefore$ Area of the square $ABCD=(Side{)}^2=8^2=64c{m}^2$
$\because$ Diagonal BD bisects the square into two triangles equal in area
Area $△ABD=\frac{1}{2}\times AreaofsquareABCD$
$=\frac{1}{2}\times 64=32c{m}^2$
$\because$ P is mid point of AB of $△ABD,$
and PQ || AD
$\therefore$ O is the mid point of BD
$\therefore OP=\frac{1}{2}AD=\frac{1}{2}\times 8=4cm\therefore Areaof△OPB=\frac{1}{2}PB\times OP=\frac{1}{2}\times 4\times 4=8c{m}^2$