The figure is made up of two squares and a triangle. The ratio of the area of Triangle E to that of Square G is 13 : 1. The ratio of the shaded area to that of the unshaded area is 1 : 5. If the difference between areas of Triangle E and Square F is 413 cm
2, what is the area of Square G?
Area of Triangle E |
Area of Square G |
Shaded area |
Unshaded area |
Total area |
13x6 |
1x6 |
|
|
13x6 |
|
|
1x13 |
5x13 |
6x13 |
78 u |
6 u |
13 u |
65 u |
78 u |
Area of Triangle E = Total area of the figure
Total area is the unchanged total. Make the total area the same.
LCM of 13 and 6 = 78
Area of Square F
= 13 u + 6 u
= 19 u
Difference between the areas of Triangle E and Square F
= 78 u - 19 u
= 59 u
59 u = 413
1 u = 413 ÷ 59 = 7
Area of Square G
= 6 u
= 6 x 7
= 42 cm
2 Answer(s): 42 cm
2