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) = ${\displaystyle \frac{1}{2}}$ × PA × QA

= ${\displaystyle \frac{1}{2}\times 30\times 50}$

∴ A(ΔPAQ) = 750 m²   ......(1)

A(ΔRCS) = ${\displaystyle \frac{1}{2}}$ × CS × RC

= ${\displaystyle \frac{1}{2}\times 60\times 25}$

∴ 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) = ${\displaystyle \frac{1}{2}}$ × PS × TB

= ${\displaystyle \frac{1}{2}\times 150\times 30=2250}$

∴ A(ΔPTS) = 2250 m²   .....(3)

QA || RC

∴ ${\displaystyle \square }$QRCA is a Trapezium.

A(${\displaystyle \square }$QRCA) = ${\displaystyle \frac{1}{2}\times \left(\text{QA + RC}\right)\times \text{AC}}$

= ${\displaystyle \frac{1}{2}\times (50+25)\times 60=\frac{1}{2}\times 75\times 60}$

∴ A(${\displaystyle \square }$QRCA) = 2250 m²   ......(4)

Area of given Plot = A(ΔPAQ) + A(${\displaystyle \square }$QRCA) + A(ΔRCS) + A(ΔPTS)

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

∴ Area of the given Plot = 6000 m²