Question

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Answer 1

Solution:

For plotting these equations on the graph, we need atleast two points for each of the two equations.

Equation 1: x + 2y = 4

→ If x = 0, y = 2

→ If y = 0, x = 4

→ Points are: (0,2), (4,0)

Equation 2: x + 2y = 8

→ If x = 0, y = 4

→ If y = 0, x = 8

→ Points are: (0,4), (8,0)

Now, refer the figure of how these equations have been plotted on the graph sheet.

Coordinates of the trapezium formed = (0,2), (0,4), (8,0), (4,0)

Area of trapezium = 1/2 × (sum of parallel sides) × height

Finding the area using this formula will be a longer method, as we will have to even find the height of the trapezium. Thus, we will go for a shorter method in which we will subtract the area of the smaller ∆ from the larger ∆.

Area of trapezium = 1/2 (b.h - b'.h')

→ Area = 1/2 (8.4 - 4.2)

→ Area = 1/2 (32 - 8) = 1/2 (24)

→ Area = 12 units²