Question

In the figure, PQRS is a square and T and U are respectively, the midpoints of PS and QR. Find the area $△OTS$ if PQ = 8 cm.

Answer 1

In square PQRS, T and U are the mid points of the sides PS and QR TU, QS and US are joined PQ = 8 cm
$\therefore$ T and U are mid - points of the opposites sides PS and QR
$\therefore TU||PQ\Rightarrow PQUTisarectangle=>PQ=TU(Oppositesideareequal.)$

The diagonal SQ bisect the line through the midpoints T an U
$\therefore TO=\frac{1}{2}\times PQ=\frac{1}{2}\times 8=4cmandTS=\frac{1}{2}\times PS=\frac{1}{2}\times 8=4cm\therefore area△OTS=\frac{1}{2}OT\times TS=\frac{1}{2}\times 4\times 4=8c{m}^2$