Area P5 2010 CA2

The attached figure is made up of two pairs of identical squares of different sizes. DCG is a straight line. The sum of the area of 1 large square and 1 small square is 52 cm2.

(a) What is the area of the shaded portion?

(b) What is the ratio of the area of triangle AHC to the area of triangle ACG?
 
 
As we may not know that 52 = 16 + 36 = (4 x 4) + (6 x 6), we will list out L x L, then look out for sum of two of the multiples that equals to 52.
L       --> 1 , 2 , 3 ,  4  .  5  ,  6
L x L --> 1 , 4 , 9 , 16 , 25 , 36
 
16 + 36 = 52    So sides of squares are 4 cm and 6 cm
 
1/2 x 4 x 6 = 12
 
12 x 2 = 24 cm2
 
a) The area of the shaded portion is 24 cm2.
 
 
1/2 x 12 x 6 = 36
 
36 : 12 = 3 : 1
 
b) The ratio of the area of triangle AHC to the area of ACG is 3 : 1.
 
 
Short cut for b) is as follows:
 
2 x 6 : 4 = 3 : 1 [Height1 : Height 2 since Base the same]