The figure is not drawn to scale. Three pentagons D, E and F are arranged as shown in the figure. The area of Pentagon D is
45 the area of Pentagon E. The area of Pentagon E is
15 the area of Pentagon F.
(a) Find the ratio of the area of Pentagon D to the area of Pentagon F.
(b)
34 of Pentagon D is shaded. What fraction of the whole figure is not shaded?
D |
E |
F |
4x1 |
5x1 |
|
|
1x5 |
5x5 |
4 u |
5 u |
25 u |
(a)
Area of Pentagon E is the repeated identity. Make the area of Pentagon E the same. LCM of 5 and 1 is 5.
Pentagon D : Pentagon F
4 : 25
(b)
Shaded part of Pentagon D
=
34 x 4 u
= 3 u
Unshaded part of Pentagon D
= 4 u - 3 u
= 1 u
Unshaded part of Pentagon F
= 25 u - 3 u
= 22 u
Total figure unshaded
= 22 u + 1 u
= 23 u
Total figure
= 25 u + 1 u
= 26 u
Fraction of the whole figure that is unshaded
=
2326Answer(s): (a) 4 : 25; (b)
2326