The figure is not drawn to scale. Three pentagons H, J and K are arranged as shown in the figure. The area of Pentagon H is ²₃ the area of Pentagon J. The area of Pentagon J is ²₅ the area of Pentagon K.
(a) Find the ratio of the area of Pentagon H to the area of Pentagon K.
(b) ³₄ of Pentagon H is shaded. What fraction of the whole figure is not shaded?

H	J	K
2x2	3x2
	2x3	5x3
4 u	6 u	15 u

(a)
Area of Pentagon J is the repeated identity. Make the area of Pentagon J the same. LCM of 3 and 2 is 6.

Pentagon H : Pentagon K
4 : 15

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

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

Unshaded part of Pentagon K
= 15 u - 3 u
= 12 u

Total figure unshaded
= 12 u + 1 u
= 13 u

Total figure
= 15 u + 1 u
= 16 u

Fraction of the whole figure that is unshaded
= ¹³₁₆

Answer(s): (a) 4 : 15; (b) ¹³₁₆