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 44 cm, and the total area of the two unshaded squares is 157 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 44 cm
2 lengths of big square + 2 lengths of small square + 2 x 5 = 44
2 lengths of big square + 2 lengths of small square + 10 = 44
2 lengths of big square + 2 lengths of small square = 44 - 10
2 x (1 length of big square + 1 length of small square) = 34
1 length of big square + 1 length of small square = 34 ÷ 2 = 17
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 17 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 |
5 |
5 x 5 = 25 |
12 |
12 x 12 = 144 |
25 +144 = 169 (X) |
7 |
7 x 7 = 49 |
10 |
10 x 10 = 100 |
49 + 100 = 149 (X) |
6 |
6 x 6 = 36 |
11 |
11 x 11 = 121 |
36 + 121 = 157 (✓) |
Length of the smaller unshaded square = 6 m
Length of the bigger unshaded square = 11 m
Total areas of the shaded right-angled triangles
= 11 x 6
= 66 m
2 Answer(s): 66 m
2