Shaded area

Haha let's use calculus. $\int_0^1 (-\frac{x}{2} + 1)dx = \boxed{\frac{3}{4}}$

$\text{Alternative geometric solution.}$

The shaded region is a trapezoid that fell on its back, oops! The area of the trapezoid is $A = h \times \frac{b_1+b_2}{2} = 1\times\frac{1 + 1/2}{2}$ $A = \boxed{\frac{3}{4}}$

Find the equations of lines and solve them simultaneously. the ordinate of the point of intersection gives the height of the smaller triangle. From the area of the bigger triangle, Subtract the area of the smaller triangle To get the required area...