$\mathrm{x}=3$ এবং $\mathrm{y}=\pm \mathrm{x}$ সরলরেখাগুলো দ্বারা আবদ্ধ ক্ষেত্রের ক্ষেত্রফল কত বর্গ একক?

The problem provides two equations that represent lines: one is x = 3, which is a vertical line at x = 3, and the other is y = ±x, which represents two lines: one with a positive slope and one with a negative slope, passing through the origin.

To find the area enclosed by these lines, we can visualize the graph:

    
• Line y = x will intersect x = 3 at the point (3, 3).
    
• Line y = -x will also intersect x = 3 at the point (3, -3).

Thus, the area is bounded by the points (3, 3), (3, -3), and the origin (0, 0). This forms a triangle:

    
• The base of the triangle stretches vertically from (3, -3) to (3, 3), which is 6 units long.
    
• The height is the horizontal distance from the y-axis (0) to the line x = 3, which is 3 units.

The area A of a triangle can be calculated using the formula:

A = (1/2) * base * height

Plugging in the values:

A = (1/2) * 6 * 3 = 9

Therefore, the answer is 9, which corresponds to option d.

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