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