The figure is not drawn to scale. Three pentagons Z, A and B are arranged as shown in the figure. The area of Pentagon Z is ⁴₅ the area of Pentagon A. The area of Pentagon A is ¹₃ the area of Pentagon B.
(a) Find the ratio of the area of Pentagon Z to the area of Pentagon B.
(b) ³₄ of Pentagon Z is shaded. What fraction of the whole figure is not shaded?

Z	A	B
4x1	5x1
	1x5	3x5
4 u	5 u	15 u

(a)
Area of Pentagon A is the repeated identity. Make the area of Pentagon A the same. LCM of 5 and 1 is 5.

Pentagon Z : Pentagon B
4 : 15

(b)
Shaded part of Pentagon Z
= ³₄ x 4 u
= 3 u

Unshaded part of Pentagon Z
= 4 u - 3 u
= 1 u

Unshaded part of Pentagon B
= 15 u - 3 u
= 12 u

Total figure unshaded
= 12 u + 1 u
= 13 u

Total figure
= 15 u + 1 u
= 16 u

Fraction of the whole figure that is unshaded
= ¹³₁₆

Answer(s): (a) 4 : 15; (b) ¹³₁₆