The figure is made up of two squares and a triangle. The ratio of the area of Triangle D to that of Square F is 11 : 1. The ratio of the shaded area to that of the unshaded area is 1 : 5. If the difference between areas of Triangle D and Square E is 490 cm
2, what is the area of Square F?
Area of Triangle D |
Area of Square F |
Shaded area |
Unshaded area |
Total area |
11x6 |
1x6 |
|
|
11x6 |
|
|
1x11 |
5x11 |
6x11 |
66 u |
6 u |
11 u |
55 u |
66 u |
Area of Triangle D = Total area of the figure
Total area is the unchanged total. Make the total area the same.
LCM of 11 and 6 = 66
Area of Square E
= 11 u + 6 u
= 17 u
Difference between the areas of Triangle D and Square E
= 66 u - 17 u
= 49 u
49 u = 490
1 u = 490 ÷ 49 = 10
Area of Square F
= 6 u
= 6 x 10
= 60 cm
2 Answer(s): 60 cm
2