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