The figure is not drawn to scale. Three pentagons F, G and H are arranged as shown in the figure. The area of Pentagon F is ⁴₅ the area of Pentagon G. The area of Pentagon G is ¹₃ the area of Pentagon H.
(a) Find the ratio of the area of Pentagon F to the area of Pentagon H.
(b) ³₄ of Pentagon F is shaded. What fraction of the whole figure is not shaded?

F	G	H
4x1	5x1
	1x5	3x5
4 u	5 u	15 u

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

Pentagon F : Pentagon H
4 : 15

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

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

Unshaded part of Pentagon H
= 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