Question

Find the area of the following field. All dimensions are in metres.

• A. $25100m^2$
• B. $28850m^2$
• C. $25300m^2$
• D. $30100m^2$

Answer 1

The correct option is D $30100m^2$

Area of the given figure = Area of $\Delta DCF$ + Area of $\Delta EGD$ + Area of trapezium FCBH + Area of $\Delta EGA$ + Area of $\Delta AHB$

$\text{Area of}\Delta DCF=\frac{1}{2}\times \text{Base}\times \text{Height}=\frac{1}{2}\times 100\times 100=\frac{10000}{2}=5000m^2$
$\text{Area of}\Delta EGD=\frac{1}{2}\times \text{Base}\times \text{Height}=\frac{1}{2}\times 120\times 180=60\times 180=10800m^2$
$\text{Area of trapezium FCBH}=\frac{1}{2}\times \text{[Sum of parallel sides]}\times \text{Height}=\frac{1}{2}\times [100+50]\times 110=\frac{1}{2}\times 150\times 110=75\times 110=8250m^2$
$\text{Area of}\Delta EGA=\frac{1}{2}\times \text{Base}\times \text{Height}=\frac{1}{2}\times 120\times 80=60\times 80=4800m^2$
$\text{Area of}\Delta AHB=\frac{1}{2}\times \text{Base}\times \text{Height}=\frac{1}{2}\times 50\times 50=25\times 50=1250m^2$

Thus, the area of the complete figure
$=5000+10800+8250+4800+1250$
$=30100m^2$