The figure is not drawn to scale. Three pentagons W, X and Y are arranged as shown in the figure. The area of Pentagon W is ⁴₅ the area of Pentagon X. The area of Pentagon X is ¹₅ the area of Pentagon Y.
(a) Find the ratio of the area of Pentagon W to the area of Pentagon Y.
(b) ³₄ of Pentagon W is shaded. What fraction of the whole figure is not shaded?

W	X	Y
4x1	5x1
	1x5	5x5
4 u	5 u	25 u

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

Pentagon W : Pentagon Y
4 : 25

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

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

Unshaded part of Pentagon Y
= 25 u - 3 u
= 22 u

Total figure unshaded
= 22 u + 1 u
= 23 u

Total figure
= 25 u + 1 u
= 26 u

Fraction of the whole figure that is unshaded
= ²³₂₆

Answer(s): (a) 4 : 25; (b) ²³₂₆