The figure is made up of two squares and a triangle. The ratio of the area of Triangle Q to that of Square S 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 Q and Square R is 490 cm
2, what is the area of Square S?
Area of Triangle Q |
Area of Square S |
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 Q = 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 R
= 13 u + 4 u
= 17 u
Difference between the areas of Triangle Q and Square R
= 52 u - 17 u
= 35 u
35 u = 490
1 u = 490 ÷ 35 = 14
Area of Square S
= 4 u
= 4 x 14
= 56 cm
2 Answer(s): 56 cm
2