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

Q	R	S
4x1	5x1
	1x5	5x5
4 u	5 u	25 u

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

Pentagon Q : Pentagon S
4 : 25

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

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

Unshaded part of Pentagon S
= 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