Question

Find the area of the field if CD = 20 m, BE = 30 m, AI = 15 m AE = 25 m, GH = 10 m, CJ = 15 m, GF = 20 m.

• A. 375 $m^2$
• B. 450 $m^2$
• C. 600 $m^2$
• D. 825 $m^2$

Answer 1

The correct option is D 825 $m^2$

Area of the field can be broken down into trapezium BCDE, $△$ABE, trapezium AGFE

Area of field = Area of trapezium BCDE + Area of $△$ABE + Area of trapezium AGFE

Area of trapezium BCDE
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height
= $\frac{1}{2}$$\times$(BE+CD)$\times$CJ = $\frac{1}{2}$$\times$(30+20)$\times$15
= $\frac{1}{2}$$\times$50$\times$15 = 25$\times$15 = 375 $m^2$

Area of trapezium AGFE
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height
= $\frac{1}{2}$$\times$(AE+GF)$\times$GH = $\frac{1}{2}$$\times$(25+20)$\times$10
= $\frac{1}{2}$$\times$45$\times$10 = 45$\times$5 = 225 $m^2$

Area of $△$ABE
= $\frac{1}{2}$$\times$base$\times$height
= $\frac{1}{2}$$\times$BE$\times$AI
= $\frac{1}{2}$$\times$30$\times$15 = 15$\times$15 = 225 $m^2$

Area of field = 375+225+225 = 825 $m^2$