Question

Find the area of the figure:

• A. 24
• B. 25
• C. 26
• D. 27

Answer 1

The correct option is C

26

Area (ABCDEF) = Area ( $\Delta$AFB) + Area (trapezium FEDB)

Observe that points E and F lie on the line x = -2 and D, B lie on x = 4.These lines are hence parallel.

Also, points E and D lie on y = 2 and hence this line through ED is perpendicular to EF and BD.

So, area of a trapezium FEDB = $\frac{1}{2}$ [(distance between parallel sides)(sum of the parallel sides)]

= $\frac{1}{2}$[ED.(EF + BD)] = $\frac{1}{2}$[(4 - (-2)) {(6 - 2) + (4 - 2)}] = $\frac{1}{2}$ [ 6 $\times$ 6] = 18 sq units

To find the area of the triangle AFB,

Suppose $x_1$= 0 , $y_1$ = 8

$x_2$= -2 , $y_2$ = 6

$x_3$= 4 , $y_3$ = 4

Area of a triangle = $\frac{1}{2}$ [$x_1$( $y_2$ - $y_3$) + $x_2$( $y_3$ - $y_1$) + $x_3$( $y_1$ - $y_2$)]

= $\frac{1}{2}$ [0(6 - 4) - 2(4 - 8) + 4(8 - 6)]

= 8 sq units

Area of a triangle = 8 sq units

Therefore, the net area = 8 + 18 = 26 sq units