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 15% of the total remaining area of both figures. If the area of the shaded part is 140 cm
2, find the remaining area of the 5-sided figure.
| |
5-sided figure |
Square |
Difference |
| Before |
4x14 =
56 u |
1x14 =
14 u |
3x14 =
42 u |
| Change |
- 5 u |
- 5 u |
|
| After |
17x3 =
51 u |
3x3 =
9 u |
14x3 =
42 u |
15% =
15100 =
320The difference in the areas remains unchanged. Make the difference in the areas the same. LCM of 3 and 14 is 42.
Area of the shaded part
= 56 u - 51 u
= 5 u
5 u = 140
1 u = 140 ÷ 5 = 28
Remaining area of the 5-sided figure
= 51 u + 9 u
= 60 u
= 60 x 28
= 1680 cm
2 Answer(s): 1680 cm
2 
