Question

Find the area of the field ABCDEFG shown in the figure, if GI, JC, FH, and GE are 1 cm, 2 cm, 4 cm, and 5 cm respectively.

• A. 20 $c{m}^2$
• B. 21 $c{m}^2$
• C. 40 $c{m}^2$
• D. 41 $c{m}^2$

Answer 1

The correct option is D 41 $c{m}^2$

Field can be divided into four simple figures ,
Trapezium ABDE, $△$BCD, $△$AGE and
$△$GFE
Hence Area of field =
Area of trapezium ABDE + Area of $△$BCD + Area of $△$AGE + Area of $△$GFE
For the trapezium ABDE
AB = 4 cm , ED = 3cm ,AE = height = 6 cm
Area of trapezium
= $\frac{1}{2}$$\times$(sum of parallel sides)$\times$height
= $\frac{1}{2}$$\times$(AB+DE)$\times$AE
= $\frac{1}{2}$$\times$(4+3)$\times$6
= $\frac{1}{2}$$\times$7$\times$6 =$\frac{7\times 6}{2}$ = 3$\times$7 = 21 $c{m}^2$

Area of triangle = $\frac{1}{2}$$\times$base$\times$height

For $△$ BCD ; base = 7 cm and height = 2 cm
Area of $△$BCD = $\frac{1}{2}$$\times$BD$\times$CJ = $\frac{1}{2}$$\times$7$\times$2
Area of $△$BCD = 7 $c{m}^2$

For $△$ AGE ; base = 6 cm and height = 1 cm

Area of $△$AGE = $\frac{1}{2}$$\times$AE$\times$GI = $\frac{1}{2}$$\times$6$\times$1
Area of $△$AGE = 3 $c{m}^2$

For $△$ GFE ; base = 5 cm and height = 4 cm
Area of $△$GFE = $\frac{1}{2}$$\times$GE$\times$FH = $\frac{1}{2}$$\times$5$\times$4
Area of $△$GFE = 10 $c{m}^2$

Area of field = 21+7+10+3 = 41 $c{m}^2$