The figure is not drawn to scale. Three pentagons N, P and Q are arranged as shown in the figure. The area of Pentagon N is ²₅ the area of Pentagon P. The area of Pentagon P is ²₅ the area of Pentagon Q.
(a) Find the ratio of the area of Pentagon N to the area of Pentagon Q.
(b) ³₄ of Pentagon N is shaded. What fraction of the whole figure is not shaded?

N	P	Q
2x2	5x2
	2x5	5x5
4 u	10 u	25 u

(a)
Area of Pentagon P is the repeated identity. Make the area of Pentagon P the same. LCM of 5 and 2 is 10.

Pentagon N : Pentagon Q
4 : 25

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

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

Unshaded part of Pentagon Q
= 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