The figure is not drawn to scale. The ratio of the area of the rectangle to the area of the circle to the area of the triangle is 20 : 9 : 3. If ¹₃ of the triangle and ¹₄ of the rectangle are shaded, what is the ratio of the total shaded area to the total of the unshaded area? Leave your answer in the simplest form.
Rectangle : Circle : Triangle
20 : 9 : 3

Area of the rectangle is the repeated identity. Use LCM to make the area of rectangle the same.

Shaded rectangle : Unshaded rectangle : Total rectangle
1 : 4 - 1 : 4
1 : 3 : 4 (x5)
5 : 15 : 20

Area of the triangle is the repeated identity. Use LCM to make the area of triangle the same.

Shaded Triangle : Unshaded Triangle : Triangle
1 : 3 - 1 : 3
1 : 2 : 3

Unshaded area
= Unshaded rectangle + Unshaded triangle + Unshaded circle
= 15 u + 2 u + (9 u - 5 u - 1 u)
= 17 u + 3 u
= 20 u

Shaded area
= 5 u + 1 u
= 6 u

Shaded area : Unshaded area
6 : 20 (÷ 2)
3 : 10

Answer(s): 3 : 10