The figure is not drawn to scale. Three pentagons T, U and V are arranged as shown in the figure. The area of Pentagon T is
25 the area of Pentagon U. The area of Pentagon U is
25 the area of Pentagon V.
(a) Find the ratio of the area of Pentagon T to the area of Pentagon V.
(b)
34 of Pentagon T is shaded. What fraction of the whole figure is not shaded?
T |
U |
V |
2x2 |
5x2 |
|
|
2x5 |
5x5 |
4 u |
10 u |
25 u |
(a)
Area of Pentagon U is the repeated identity. Make the area of Pentagon U the same. LCM of 5 and 2 is 10.
Pentagon T : Pentagon V
4 : 25
(b)
Shaded part of Pentagon T
=
34 x 4 u
= 3 u
Unshaded part of Pentagon T
= 4 u - 3 u
= 1 u
Unshaded part of Pentagon V
= 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