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
25 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 |
4x2 |
5x2 |
|
|
2x5 |
5x5 |
8 u |
10 u |
25 u |
(a)
Area of Pentagon N is the repeated identity. Make the area of Pentagon N the same. LCM of 5 and 2 is 10.
Pentagon M : Pentagon P
8 : 25
(b)
Shaded part of Pentagon M
=
34 x 8 u
= 6 u
Unshaded part of Pentagon M
= 8 u - 6 u
= 2 u
Unshaded part of Pentagon P
= 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