The figure is not drawn to scale. Three pentagons X, Y and Z are arranged as shown in the figure. The area of Pentagon X is ⁴₅ the area of Pentagon Y. The area of Pentagon Y is ¹₇ the area of Pentagon Z.
(a) Find the ratio of the area of Pentagon X to the area of Pentagon Z.
(b) ³₄ of Pentagon X is shaded. What fraction of the whole figure is not shaded?

X	Y	Z
4x1	5x1
	1x5	7x5
4 u	5 u	35 u

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

Pentagon X : Pentagon Z
4 : 35

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

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

Unshaded part of Pentagon Z
= 35 u - 3 u
= 32 u

Total figure unshaded
= 32 u + 1 u
= 33 u

Total figure
= 35 u + 1 u
= 36 u

Fraction of the whole figure that is unshaded
= ³³₃₆
= ¹¹₁₂

Answer(s): (a) 4 : 35; (b) ¹¹₁₂