The figure is not drawn to scale. Three pentagons K, L and M are arranged as shown in the figure. The area of Pentagon K is
45 the area of Pentagon L. The area of Pentagon L is
15 the area of Pentagon M.
(a) Find the ratio of the area of Pentagon K to the area of Pentagon M.
(b)
34 of Pentagon K is shaded. What fraction of the whole figure is not shaded?
K |
L |
M |
4x1 |
5x1 |
|
|
1x5 |
5x5 |
4 u |
5 u |
25 u |
(a)
Area of Pentagon L is the repeated identity. Make the area of Pentagon L the same. LCM of 5 and 1 is 5.
Pentagon K : Pentagon M
4 : 25
(b)
Shaded part of Pentagon K
=
34 x 4 u
= 3 u
Unshaded part of Pentagon K
= 4 u - 3 u
= 1 u
Unshaded part of Pentagon M
= 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