The figure is made up of two squares and a triangle. The ratio of the area of Triangle S to that of Square U is 13 : 1. The ratio of the shaded area to that of the unshaded area is 1 : 3. If the difference between areas of Triangle S and Square T is 455 cm
2, what is the area of Square U?
Area of Triangle S |
Area of Square U |
Shaded area |
Unshaded area |
Total area |
13x4 |
1x4 |
|
|
13x4 |
|
|
1x13 |
3x13 |
4x13 |
52 u |
4 u |
13 u |
39 u |
52 u |
Area of Triangle S = Total area of the figure
Total area is the unchanged total. Make the total area the same.
LCM of 13 and 4 = 52
Area of Square T
= 13 u + 4 u
= 17 u
Difference between the areas of Triangle S and Square T
= 52 u - 17 u
= 35 u
35 u = 455
1 u = 455 ÷ 35 = 13
Area of Square U
= 4 u
= 4 x 13
= 52 cm
2 Answer(s): 52 cm
2