The figure is not drawn to scale. Three pentagons S, T and U are arranged as shown in the figure. The area of Pentagon S is ⁴₅ the area of Pentagon T. The area of Pentagon T is ¹₇ the area of Pentagon U.
(a) Find the ratio of the area of Pentagon S to the area of Pentagon U.
(b) ³₄ of Pentagon S is shaded. What fraction of the whole figure is not shaded?

S	T	U
4x1	5x1
	1x5	7x5
4 u	5 u	35 u

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

Pentagon S : Pentagon U
4 : 35

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

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

Unshaded part of Pentagon U
= 35 u - 3 u
= 32 u

Total figure unshaded
= 32 u + 1 u
= 33 u

Total figure
= 35 u + 1 u
= 36 u

Fraction of the whole figure that is unshaded
= ³³₃₆
= ¹¹₁₂

Answer(s): (a) 4 : 35; (b) ¹¹₁₂