The figure is not drawn to scale. Three pentagons M, N and P are arranged as shown in the figure. The area of Pentagon M is
45 the area of Pentagon N. The area of Pentagon N is
13 the area of Pentagon P.
(a) Find the ratio of the area of Pentagon M to the area of Pentagon P.
(b)
34 of Pentagon M is shaded. What fraction of the whole figure is not shaded?
M |
N |
P |
4x1 |
5x1 |
|
|
1x5 |
3x5 |
4 u |
5 u |
15 u |
(a)
Area of Pentagon N is the repeated identity. Make the area of Pentagon N the same. LCM of 5 and 1 is 5.
Pentagon M : Pentagon P
4 : 15
(b)
Shaded part of Pentagon M
=
34 x 4 u
= 3 u
Unshaded part of Pentagon M
= 4 u - 3 u
= 1 u
Unshaded part of Pentagon P
= 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