Find the area of the given trapezium PQRS in which RQ || SP and PQ `bot` SP such that RQ = 7m, RS = 13 m and SP = 12 m.

Explanation

Draw RT `bot` SP. Then, TP = RQ = 7 m.
`therefore" "ST = SP - TP = (12 - 7)`m = 5 m.
From right `Delta`RTS, we have
`RT^(2)=RS^(2)-ST^(2)=[(13 m)^(2)-(5 m)^(2)]`
`=(169 - 25)m^(2) = 144 m^(2)`
`therefore" "RT = sqrt(144)`m = 12 m.
Area of trap. PQRS
`=((1)/(2)xx "sum of parallel siles"xx"distance between them")`
`={(1)/(2)xx(RQ + SP)xx RT}`sq units
`={(1)/(2)xx(7 + 12)xx12}m^(2)=(19 xx 6)m^(2) = 144 m^(2)`.
Hence, the area of the trapezium PQRS is 114 `m^(2)`.