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)]
$=\frac{1}{2}\left[ED\right(EF+BD\left)\right]=\frac{1}{2}\left(\right(4-(-2)\left)\right\{(6-2)+(4-2)\}=\frac{1}{2}[6\times 6]=18squnits$

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

Area of a triangle = 8 sq units.

Therefore, the total area = 8 + 18 = 26 sq units.