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Question

Find the area of the figure:


A
24
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B
25
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C
26
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D
27
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Solution

The correct option is C 26

Area (ABCDEF) = Area ( ΔAFB) + 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 = 12 [(distance between parallel sides)(sum of the parallel sides)]
=12[ED(EF+BD)]=12((4(2)){(62)+(42)}=12[6×6]=18 sq units

To find the area of the triangle AFB,

Suppose x1= 0 , y1 = 8

x2= -2 , y2 = 6

x3= 4 , y3 = 4

Area of a triangle =12 [x1( y2 - y3) + x2( y3 - y1) + x3( y1 - y2)]

= 12 [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.


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