The figure, not drawn to scale, is made up of two identical right-angled triangles, a small square and a big square. The lengths of the 2 squares are whole numbers.  The perimeter of the shaded region is 64 cm, and the total area of the two unshaded squares is 410 m². Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 64 cm

2 lengths of big square + 2 lengths of small square + 2 x 6 = 64
2 lengths of big square + 2 lengths of small square + 12 =  64 
2 lengths of big square + 2 lengths of small square = 64 - 12 
2 x (1 length of big square + 1 length of small square) = 52

1 length of big square + 1 length of small square = 52 ÷ 2 = 26

Use guess and check. 
Total length of the smaller unshaded square and bigger unshaded square must be 26 m.

Length of the smaller unshaded square	Area of the smaller unshaded square	Length of the bigger unshaded square	Area of the bigger unshaded square	Total unshaded squares
6	6 x 6 =  36	20	20 x 20 = 400	36 +400 =  436 (X)
8	8 x 8 = 64	18	18 x 18 = 324	64 + 324 = 388 (X)
7	7 x 7 = 49	19	19 x 19  = 361	49  + 361 = 410 (✓)

Length of the smaller unshaded square = 7 m
Length of the bigger unshaded square = 19 m

Total areas of the shaded right-angled triangles
= 19 x 7
= 133 m²

Answer(s): 133 m²