The figure shows an irregular 5-sided figure and a square not drawn to scale. The area of the five-sided figure was thrice 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 84 cm
2, find the remaining area of the 5-sided figure.
|
5-sided figure |
Square |
Difference |
Before |
3x4 = 12 u |
1x4 = 4 u |
2x4 = 8 u |
Change |
- 3 u |
- 3 u |
|
After |
9x1 = 9 u |
1x1 = 1 u |
8x1 = 8 u |
10% =
10100 =
110The difference in the areas remains unchanged. Make the difference in the areas the same. LCM of 2 and 8 is 8.
Area of the shaded part
= 12 u - 9 u
= 3 u
3 u = 84
1 u = 84 ÷ 3 = 28
Remaining area of the 5-sided figure
= 9 u + 1 u
= 10 u
= 10 x 28
= 280 cm
2 Answer(s): 280 cm
2