The area of the region (\\{ {(x, y): 0 ≤ x ≤ \frac{9}{4}, 0... | Mathematics | SolveeIt | Solveeit

Today, August 24

Question

The area of the region $\\{ {(x, y): 0 ≤ x ≤ \frac{9}{4}, 0 ≤ y ≤ 1, x ≥ 3y, x + y ≥ 2}\\}$

A

$\frac{11}{32}$

B

$\frac{35}{96}$

C

$\frac{37}{96}$

D

$\frac{13}{32}$

Answer

$\frac{11}{32}$

Explanation

Solution

area of triangle
Area of required region
$=\frac{1}{2} (\frac{2}{3}+\frac{3}{4})\frac{1}{4}+\frac{1}{2} \times\frac{2}{3} \times\frac{1}{2}$
$=\frac{11}{32}$