Question

Find the areas of the given plot. (All measures are in metres.)

Answer 1

In given Figure,

PA = 30 m, AB = 30 m BC = 30 m, CS = 60 m, QA = 50 m, RC = 25 m, TB = 30 m.

A(ΔPAQ) = `1/2` × PA × QA

= `1/2 xx 30 xx 50`

∴ A(ΔPAQ) = 750 m²   ......(1)

A(ΔRCS) = `1/2` × CS × RC

= `1/2 xx 60 xx 25`

∴ A(ΔRCS) = 750 m²   ......(2)

∵ P − A − B − C − S

∴ PS = PA + AB + BC + CS

= 30 + 30 + 30 + 60

∴ PS = 150 m

Also, AC = AB + BC = 30 + 30 = 60 m

Also, AC = AB + BC = 30 + 30 = 60 m

A(ΔPTS) = `1/2` × PS × TB

= `1/2 xx 150 xx 30 = 2250`

∴ A(ΔPTS) = 2250 m²   .....(3)

QA || RC

∴ `square`QRCA is a Trapezium.

A(`square`QRCA) = `1/2 xx ("QA + RC") xx "AC"`

= `1/2 xx (50 + 25) xx 60 = 1/2 xx 75 xx 60`

∴ A(`square`QRCA) = 2250 m²   ......(4)

Area of given Plot = A(ΔPAQ) + A(`square`QRCA) + A(ΔRCS) + A(ΔPTS)

= 750 + 2250 + 750 + 2250    .......[From (1), (2), (3) and (4)]

∴ Area of the given Plot = 6000 m²