Question:
The area of the triangle formed by the lines y = x, x = 6 and y = 0 is
(a) 36 sq. units
(b) 18 sq. units
(c) 9 sq. units
(d) 72 sq. units
Solution:
Given $x=6, y=0$ and $x=y$
We have plotting points as $(6,0)(0,0)(6,6)$ when $x=y$
Therefore, area of $\triangle A B C=\frac{1}{2}($ Base $\times$ Height $)=\frac{1}{2}(C A \times A B)=\frac{1}{2}(6 \times 6)=\frac{1}{2} \times 36=18$
Area of triangle $A B C$ is 18 square units
Hence, the correct choice is $b$