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

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30400

m²

3000

m²

30100

m²

31100

m²

answer is C.

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Detailed Solution

Given is a figure,
Question Image

We are given a figure to find all dimensions in meters.
Divide the figure in

3

triangles and 1 trapezium.
Triangles: ADE , AHB and DFC.
Trapezium: BHFC.
Use formula for area of triangle:

Area = 12 B a s e h e i g h t

Substitute AD=

50 + 30 + 80 + 100

and GE is 120 to find area of triangle ADE.
Area of

△ A D E = 12 50 + 30 + 80 + 100 120

\Rightarrow

Area of

∆ ADE

=15600
Substitute AH and BH = 50 to find area of triangle ABH.

\Rightarrow

Area of

△ A B H = 125050 = 1250

Substitute DF and FC = 100 to find area of triangle DFC.

\Rightarrow

Area of

△ A B H = 12100100 = 5000

Use formula for area of trapezium BHFC.

\Rightarrow

Area of trapezium BHFC

= \frac{1}{2}

(BH+FC)

\times FH

Substitute

B H = 50, F C = 100 and FH = 30 + 80

to find area.
Area of Trapezium

= 12 50 + 100 30 + 80

\Rightarrow

Area of trapezium = 8250
Add all areas to find area of the figure.
Area

= 15600 + 1250 + 5000 + 8250

\Rightarrow

Area =

30100 m 2

So, the area of the given figure is

30100

m².
Hence, correct option is 3.

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