The figure is not drawn to scale. Three pentagons V, W and X are arranged as shown in the figure. The area of Pentagon V is
45 the area of Pentagon W. The area of Pentagon W is
25 the area of Pentagon X.
(a) Find the ratio of the area of Pentagon V to the area of Pentagon X.
(b)
34 of Pentagon V is shaded. What fraction of the whole figure is not shaded?
V |
W |
X |
4x2 |
5x2 |
|
|
2x5 |
5x5 |
8 u |
10 u |
25 u |
(a)
Area of Pentagon W is the repeated identity. Make the area of Pentagon W the same. LCM of 5 and 2 is 10.
Pentagon V : Pentagon X
8 : 25
(b)
Shaded part of Pentagon V
=
34 x 8 u
= 6 u
Unshaded part of Pentagon V
= 8 u - 6 u
= 2 u
Unshaded part of Pentagon X
= 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=
79Answer(s): (a) 8 : 25; (b)
79