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
23 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 |
2x2 |
3x2 |
|
|
2x3 |
5x3 |
4 u |
6 u |
15 u |
(a)
Area of Pentagon Y is the repeated identity. Make the area of Pentagon Y the same. LCM of 3 and 2 is 6.
Pentagon X : Pentagon Z
4 : 15
(b)
Shaded part of Pentagon X
=
34 x 4 u
= 3 u
Unshaded part of Pentagon X
= 4 u - 3 u
= 1 u
Unshaded part of Pentagon Z
= 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
=
1316Answer(s): (a) 4 : 15; (b)
1316