Question

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


[4 marks]

Answer 1

Area of the △EFH $=\frac{1}{2}\times b\times h$
$=\frac{1}{2}\times 40\times 80$
$=20\times 80$
$=1600$ m${}^2$

[0.5 mark]

Area of the rectangle EDCI $=l\times b$
$=(80+80)\times 100$
$=160\times 100$
$=16000$ m${}^2$

[0.5 mark]

Area of the trapezium FHJG = $\frac{1}{2}\times h\times (a+b)$
$=\frac{1}{2}\times (80+80)\times (160+40)$
$=\frac{1}{2}\times 160\times 200$
$=80\times 200$
$=16000$ m${}^2$

[0.5 mark]

Area of the trapezium ICBK $=\frac{1}{2}\times h\times (a+b)$
$=\frac{1}{2}\times (80+40)\times (100+60)$
$=\frac{1}{2}\times 120\times 160$
$=60\times 160$
$=9600$ m${}^2$

[0.5 mark]

Area of the △GJA $=\frac{1}{2}\times b\times h$
$=\frac{1}{2}\times 160\times (40+60)$
$=80\times 100$
$=8000$ m${}^2$

[0.5 mark]

Area of the △KBA $=\frac{1}{2}\times b\times h$
$=\frac{1}{2}\times 60\times 60$
$=30\times 60$
$=1800$ m${}^2$

[0.5 mark]


Area of the polygon is the sum of the areas of all the quadrilaterals and triangles.

Area of the polygon $=1600+16000+16000+9600+8000+1800$
$=53000$ m${}^2$

[1 mark]