Problem Solving

What is the area of shaded region in the figure shown?

A. 4/3
B. 8/3
C. 4
D. 8
E. 12

The OA is E .

How can I find the value of the base of the triangle? Experts, may you help me?

Hello Vjesus12.

You have to calculate the slope of the line: $$m=\frac{y_1-y_0}{x_1-x_0}=\frac{1-0}{0-\frac{-8}{3}}=\frac{1}{\frac{8}{3}}=\frac{3}{8}.$$ Now, the equation of the line is $$y=mx+b=\frac{3}{8}x+1.$$ Finaly, we replace y=4 in the equation of the line: $$4=\frac{3}{8}x+1\ \ \leftrightarrow\ 3=\frac{3}{8}x\ \leftrightarrow\ \ x=8.$$ So, the base of the triangle is 8 and its height is 3. So, its area is $$A=\frac{8\cdot3}{2}=12.$$ The correct answer is E.

I hope this explanation can help you.

Feel free to ask me again if you have a doubt.

Regards.