Question

PQRS is a parallelogram. X and Y are mid-point of sides PQ and RS respectively. If W and Z are point on intersection of SX & PY and XR & YQ respectively. Then show that ar (triangle YWZ) =ar ( triangle XWZ)

Answer 1

Given PQRS is a parallelogram X and Y are mid points of PQ and SR respectively and PS || XY || QR
Construction Draw $SM\perp PQ$
Now Area || gm XQRY Area || gm PQRS = $XQ\times SMPQ\times SM=12PQPQ=12$
\therefore Area || gm XQRY = 12 area || gm PQRS = $12\times 24c{m}^2=12c{m}^2$
Now area || gm XQYS area || gm XQRY = $XQ\times SMXQ\times SM=1$
$\therefore$ area || gm XQYS = area || gm XQRY = $12c{m}^2$.