Ratio P6

In the figure below, which is not drawn to scale, 1/3 of the circle is shaded, 1/5 of the triangle is shaded and 1/4 of the rectangle is shaded. The total area of the circle and triangle is 7/8 of the rectangle. Given that the total area of the whole figure is 260 cm2, find the area of the rectangle.

C + T : R = 7 : 8 = 14 : 16  Multiply by 2 to make (C + T) the same
7 x ? = 3 x ? + 5 x ?  [7 x 2 = 3 x 3 + 5 x 1 Guess and Check]

CS : C = 1 : 3 = 3 : 9   Multiply by 3 to make (C + T) the same

TS : T = 1 : 5

RS : R = 1 : 4 = 4 : 16  Multiply by 4 to get R = 16

C + T + R --> 14 + 16 - 3 - 1 = 26

26 u --> 260
1 u --> 260/26 = 10

16 u --> 16 x 10 = 160 cm2.

The area of the rectangle is 160 cm2.



Alternative method [Given informations 1/3 and 1/5 are redundant]

C + T : R = 7 : 8

RS : R = 1 : 4 = 2 : 8

7 + 8 - 2 = 13    Minus 2 to remove double-counting of shaded areas.

13 u --> 260
1 u --> 260/13 = 20

8 u --> 8 x 20 = 160 cm2.

The area of the rectanglee is 160 cm2.