Question

What is the area of the region bounded by the lines $x=y,y=0$ and $x=4$?

• A. $4$ square units
• B. $8$ square units
• C. $12$ square units
• D. $16$ square units

Answer 1

The correct option is B $8$ square units

The region bounded by $x=y,y=0$ and $x=4$ is the triangle $OAB$ as shown in the figure.
Co-ordinate of $A$ is $(4,4)$
Length of $AB$ is $4$ unit.

Since, the bounded area is a triangle. So, we have
Area of the bounded region $=\frac{1}{2}\times AB\times OB=\frac{1}{2}\cdot 4\cdot 4=8$
Option B is correct