The figure shows an irregular 5-sided figure and a square not drawn to scale. The area of the five-sided figure was four times the area of the square. After the shaded part was removed, the area of the remaining square became 10% of the total remaining area of both figures. If the area of the shaded part is 165 cm
2, find the remaining area of the 5-sided figure.
|
5-sided figure |
Square |
Difference |
Before |
4x8 = 32 u |
1x8 = 8 u |
3x8 = 24 u |
Change |
- 5 u |
- 5 u |
|
After |
9x3 = 27 u |
1x3 = 3 u |
8x3 = 24 u |
10% =
10100 =
110The difference in the areas remains unchanged. Make the difference in the areas the same. LCM of 3 and 8 is 24.
Area of the shaded part
= 32 u - 27 u
= 5 u
5 u = 165
1 u = 165 ÷ 5 = 33
Remaining area of the 5-sided figure
= 27 u + 3 u
= 30 u
= 30 x 33
= 990 cm
2 Answer(s): 990 cm
2