The figure is made up of two squares and a triangle. The ratio of the area of Triangle K to that of Square M is 11 : 1. The ratio of the shaded area to that of the unshaded area is 1 : 3. If the difference between areas of Triangle K and Square L is 551 cm
2, what is the area of Square M?
Area of Triangle K |
Area of Square M |
Shaded area |
Unshaded area |
Total area |
11x4 |
1x4 |
|
|
11x4 |
|
|
1x11 |
3x11 |
4x11 |
44 u |
4 u |
11 u |
33 u |
44 u |
Area of Triangle K = Total area of the figure
Total area is the unchanged total. Make the total area the same.
LCM of 11 and 4 = 44
Area of Square L
= 11 u + 4 u
= 15 u
Difference between the areas of Triangle K and Square L
= 44 u - 15 u
= 29 u
29 u = 551
1 u = 551 ÷ 29 = 19
Area of Square M
= 4 u
= 4 x 19
= 76 cm
2 Answer(s): 76 cm
2