Question

Find the area of the given field. (All dimensions are in metres)
[3 Marks]

Answer 1

We can easily notice by looking at the figure of the given polygon that it is a combination of three triangles and two trapeziums.

Triangles: △DME, △DNC, △FOA
Trapezium: EMOF, NCBA
Note: DM = 40 m, DN = 80 m, MO = 70 m, NA = 80 m

[0.5 Marks]

ar(△DME) = $\frac{1}{2}$ × 60 × 40 = 1200 cm${}^2$
ar(△DNC) = $\frac{1}{2}$ × 80 × 40 = 1600 cm${}^2$
ar(△FOA) = $\frac{1}{2}$ × 50 × 50 = 1250 cm${}^2$
ar(EMOF) = $\frac{1}{2}$ × 70 × (50 + 60) = 3850 cm${}^2$
ar(NCBA) = $\frac{1}{2}$ × 80 × (40 + 30) = 2800 cm${}^2$

[1.5 Marks]

Total area = 1200 + 1600 + 1250 + 3850 + 2800 = 10700 cm${}^2$

[1 Mark]