Question

Find the area of each of the following figure:

Answer 1

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.