Question

PQRS is a square. T and U are respectively, the mid-points of PS and QR (Fig.). Find the area of ∆ OTS, if PQ = 8 cm, where O is the point of intersection of TU and QS.

Answer 1

PS = PQ = 8 cm and TU || PQ 

ST = 1/2 PS = 1/2 × 8 = 4 cm 

PQ = TU = 8 cm

OT = 1/2 TU = 1/2 × 8 = 4 cm 

Area of triangle OTS 

= 1/2 × ST × OT [Since OTS is a right angled triangle] 

= 1/2  × 4 × 4 cm² = 8 cm²