The figure is made up of two squares and a triangle. The ratio of the area of Triangle H to that of Square K 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 H and Square J is 544 cm
2, what is the area of Square K?
Area of Triangle H |
Area of Square K |
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 H = 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 J
= 7 u + 4 u
= 11 u
Difference between the areas of Triangle H and Square J
= 28 u - 11 u
= 17 u
17 u = 544
1 u = 544 ÷ 17 = 32
Area of Square K
= 4 u
= 4 x 32
= 128 cm
2 Answer(s): 128 cm
2