In the figure, not drawn to scale, 40% of the triangle EHG is shaded. The ratio of the shaded part of the circle to the unshaded part of the circle is 7 : 9. What percentage of the rectangle DEGF is unshaded?
Shaded Circle |
Unshaded Circle |
Shaded Triangle |
Total Triangle |
7x2 |
9x2 |
2x7 |
5x7 |
14 u |
18 u |
14 u |
35 u |
40% =
40100 =
25 The shaded part of the figure is the repeated identity. Make the shaded part of the figure the same. LCM of 2 and 7 is 14.
Total area of the rectangle
= 2 x Total triangle
= 2 x 35 u
= 70 u
Unshaded areas
= 70 u - 14 u
= 56 u
Percentage of Rectangle DEGF that is unshaded
=
Unshaded areasArea of Rectangle DEGF x 100%
=
5670 x 100%
= 80%
Answer(s): 80%