The figure is not drawn to scale. Three pentagons P, Q and R are arranged as shown in the figure. The area of Pentagon P is
45 the area of Pentagon Q. The area of Pentagon Q is
17 the area of Pentagon R.
(a) Find the ratio of the area of Pentagon P to the area of Pentagon R.
(b)
34 of Pentagon P is shaded. What fraction of the whole figure is not shaded?
P |
Q |
R |
4x1 |
5x1 |
|
|
1x5 |
7x5 |
4 u |
5 u |
35 u |
(a)
Area of Pentagon Q is the repeated identity. Make the area of Pentagon Q the same. LCM of 5 and 1 is 5.
Pentagon P : Pentagon R
4 : 35
(b)
Shaded part of Pentagon P
=
34 x 4 u
= 3 u
Unshaded part of Pentagon P
= 4 u - 3 u
= 1 u
Unshaded part of Pentagon R
= 35 u - 3 u
= 32 u
Total figure unshaded
= 32 u + 1 u
= 33 u
Total figure
= 35 u + 1 u
= 36 u
Fraction of the whole figure that is unshaded
=
3336=
1112Answer(s): (a) 4 : 35; (b)
1112