In the below figure, PQRS is a square and T and U are respectively, the mid-points of PS
and QR. Find the area of ΔOTS if PQ = 8 cm.
From the figure
T and U are the midpoints of PS and QR respectively.
∴ TU || PQ
⇒ TO || PQ
Thus, in ΔPQS,T is the midpoint of PS and TO || PQ
∴ TO = `1/2` PQ = 4cm
Also , TS = `1/2`PS = 4cm
∴ `ar (ΔOTS) =1/2 (TOxx TS) = 1/2 (4xx4) cm ^2 = 8 cm ^2`
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- Corollary: A rectangle and a parallelogram on the same base and between the same parallels are equal in area.