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Question
Find the area of each of the following figure:
Solution
Construction: Draw TM ⊥ QS
Area of ΔRQS
= `(1)/(2) xx "QS" xx "RN"`
= `(1)/(2) xx 35 xx 20`
= 350cm2
Now,
S = QM + MS
⇒ 35 = 25 + MS
⇒ MS = 10cm
In ΔSTM,
MS2 + TM2 = ST2
⇒ TM2 = ST2 - MS2
= (26)2 - (10)2
= 676 - 100
= 576
⇒ TM
= 24cm
= PQ
Area of trapezium PQST
= `(1)/(2) xx ("PT" + "QS") xx "PQ"`
= `(1)/(2) xx (25 + 35) xx 24`
= 720cm2
Thus, area of given figure
= Area of ΔRQS + Area of trapezium PQST
=350cm2 + 720cm2
= 1070cm2.
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