The figure is made up of two squares and a triangle. The ratio of the area of Triangle X to that of Square Z is 7 : 1. The ratio of the shaded area to that of the unshaded area is 1 : 3. If the difference between areas of Triangle X and Square Y is 459 cm
2, what is the area of Square Z?
Area of
Triangle X |
Area of
Square Z |
Shaded
area |
Unshaded
area |
Total
area |
| 7x4 |
1x4 |
|
|
7x4 |
| |
|
1x7 |
3x7 |
4x7 |
| 28 u |
4 u |
7 u |
21 u |
28 u |
Area of Triangle X = Total area of the figure
Total area is the unchanged total. Make the total area the same.
LCM of 7 and 4 = 28
Area of Square Y
= 7 u + 4 u
= 11 u
Difference between the areas of Triangle X and Square Y
= 28 u - 11 u
= 17 u
17 u = 459
1 u = 459 ÷ 17 = 27
Area of Square Z
= 4 u
= 4 x 27
= 108 cm
2 Answer(s): 108 cm
2 
