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Q.

Find the area of the quadrilateral formed by the lines y = -1, y = 3 and $4 x − y = 5$ and the y -axis.

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a

Area of quadrilateral = 16 Sq. unit

b

Area of quadrilateral = 12 Sq. unit

c

Area of quadrilateral = 18 Sq. unit

d

Area of quadrilateral = 8 Sq. unit

answer is D.

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Detailed Solution

Given lines are

y = − 1

…………(1)

y = 3

……………(2)

4 x − y = 5

…..(3)
Use the information provided, equation (1) indicates a straight line parallel to the x-axis and at a distance of one unit on the downward x-axis's side.
Equation (2) indicates a straight line parallel to the x-axis and three units above the x-axis.
Find the points on x and y-axis.
Consider equation (3).

− y = 5 − 4 x

y = 4 x − 5

………….(4)
Put x =0 in equation (4)

y = 40 − 5

y = − 5

Put x=1 in equation (4)

y = 41 − 5

y = 4 − 5

y = − 1

Put x=2 in equation (4)

y = 42 − 5

y = 8 − 5

y = 3

x	0	1	2
y	-5	-1	3

The graph after plotting the given lines is shown below.
Question Image

Question Image

We know that,
Area of trapezium ABCD

= 12 A B + C D × A C .

From graph,

A C = 4, A B = 3, C D = 1.

Area of trapezium ABCD

= 12 3 + 1 × 4

= 124 × 4

= 2 × 4

= 8 sq. unit
Area of quadrilateral ABCD = 8 square unit.
The correct option is (4).

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