The figure is not drawn to scale. Three pentagons U, V and W are arranged as shown in the figure. The area of Pentagon U is ⁴₅ the area of Pentagon V. The area of Pentagon V is ²₅ the area of Pentagon W.
(a) Find the ratio of the area of Pentagon U to the area of Pentagon W.
(b) ³₄ of Pentagon U is shaded. What fraction of the whole figure is not shaded?

U	V	W
4x2	5x2
	2x5	5x5
8 u	10 u	25 u

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

Pentagon U : Pentagon W
8 : 25

(b)
Shaded part of Pentagon U
= ³₄ x 8 u
= 6 u

Unshaded part of Pentagon U
= 8 u - 6 u
= 2 u

Unshaded part of Pentagon W
= 25 u - 6 u
= 19 u

Total figure unshaded
= 19 u + 2 u
= 21 u

Total figure
= 25 u + 2 u
= 27 u

Fraction of the whole figure that is unshaded
= ²¹₂₇
= ⁷₉

Answer(s): (a) 8 : 25; (b) ⁷₉