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

K	L	M
2x2	3x2
	2x3	5x3
4 u	6 u	15 u

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

Pentagon K : Pentagon M
4 : 15

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

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

Unshaded part of Pentagon M
= 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