The figure shows an irregular 5-sided figure and a square not drawn to scale. The area of the five-sided figure was twice the area of the square. After the shaded part was removed, the area of the remaining square became 20% of the total remaining area of both figures. If the area of the shaded part is 72 cm
2, find the remaining area of the 5-sided figure.
|
5-sided figure |
Square |
Difference |
Before |
2x3 = 6 u |
1x3 = 3 u |
1x3 = 3 u |
Change |
- 2 u |
- 2 u |
|
After |
4x1 = 4 u |
1x1 = 1 u |
3x1 = 3 u |
20% =
20100 =
15The difference in the areas remains unchanged. Make the difference in the areas the same. LCM of 1 and 3 is 3.
Area of the shaded part
= 6 u - 4 u
= 2 u
2 u = 72
1 u = 72 ÷ 2 = 36
Remaining area of the 5-sided figure
= 4 u + 1 u
= 5 u
= 5 x 36
= 180 cm
2 Answer(s): 180 cm
2