3. The diagram shows the square $P Q R S$ and $T$, the mid-point of the side $P Q$. What fraction of the area of the square $P Q R S$ is shaded?
A $\frac{1}{4}$
B $\frac{1}{3}$
C $\frac{1}{2}$
D $\frac{2}{3}$
E $\frac{3}{4}$
3. A As $T$ is the midpoint of the side $P Q, P T=T Q$. Therefore triangles $P R T$ and $T R Q$ have equal bases and the same perpendicular height, namely $Q R$. So they are equal in area. Hence the shaded area is half the area of triangle $P Q R$, which in turn is half the area of the square $P Q R S$.
Therefore the required fraction is $\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}$.