In the figure, not drawn to scale, 20% of the triangle EHG is shaded. The ratio of the shaded part of the circle to the unshaded part of the circle is 4 : 9. What percentage of the rectangle DEGF is unshaded?
Shaded
Circle |
Unshaded
Circle |
Shaded
Triangle |
Total
Triangle |
| 4x1 |
9x1 |
1x4 |
5x4 |
| 4 u |
9 u |
4 u |
20 u |
20% =
20100 =
15 The shaded part of the figure is the repeated identity. Make the shaded part of the figure the same. LCM of 1 and 4 is 4.
Total area of the rectangle
= 2 x Total triangle
= 2 x 20 u
= 40 u
Unshaded areas
= 40 u - 4 u
= 36 u
Percentage of Rectangle DEGF that is unshaded
=
Unshaded areasArea of Rectangle DEGF x 100%
=
3640 x 100%
= 90%
Answer(s): 90%
