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

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

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

Pentagon P : Pentagon R
4 : 25

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

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

Unshaded part of Pentagon R
= 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