Question 9
a) The first diagram combines a triangle, a circle and a square of equal area. The shaded regions are the overlaps shown. The unshaded part of the triangle is $5/8$ of the whole triangle, and half the circle is shaded. Find the ratio of the unshaded area to the area of the entire combined figure.
b) In the second diagram, triangle $PQR$ has all three sides equal to 3 cm. Points $U,V,W,X,Y,Z$ divide the sides into 1 cm segments as shown. Find the ratio of the shaded area to the area of triangle $PQR$.
Label clarification: $W$, the left division point on $QR$, is included explicitly in the list of marked points.
b) In the second diagram, triangle $PQR$ has all three sides equal to 3 cm. Points $U,V,W,X,Y,Z$ divide the sides into 1 cm segments as shown. Find the ratio of the shaded area to the area of triangle $PQR$.
Label clarification: $W$, the left division point on $QR$, is included explicitly in the list of marked points.