The figure is made up of two squares and a triangle. The ratio of the area of Triangle P to that of Square R is 7 : 1. The ratio of the shaded area to that of the unshaded area is 1 : 5. If the difference between areas of Triangle P and Square Q is 580 cm
2, what is the area of Square R?
Area of Triangle P |
Area of Square R |
Shaded area |
Unshaded area |
Total area |
7x6 |
1x6 |
|
|
7x6 |
|
|
1x7 |
5x7 |
6x7 |
42 u |
6 u |
7 u |
35 u |
42 u |
Area of Triangle P = Total area of the figure
Total area is the unchanged total. Make the total area the same.
LCM of 7 and 6 = 42
Area of Square Q
= 7 u + 6 u
= 13 u
Difference between the areas of Triangle P and Square Q
= 42 u - 13 u
= 29 u
29 u = 580
1 u = 580 ÷ 29 = 20
Area of Square R
= 6 u
= 6 x 20
= 120 cm
2 Answer(s): 120 cm
2