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 48 cm, and the total area of the two unshaded squares is 193 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 48 cm
2 lengths of big square + 2 lengths of small square + 2 x 5 = 48
2 lengths of big square + 2 lengths of small square + 10 = 48
2 lengths of big square + 2 lengths of small square = 48 - 10
2 x (1 length of big square + 1 length of small square) = 38
1 length of big square + 1 length of small square = 38 ÷ 2 = 19
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 19 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 |
13 |
13 x 13 = 169 |
36 +169 = 205 (X) |
8 |
8 x 8 = 64 |
11 |
11 x 11 = 121 |
64 + 121 = 185 (X) |
7 |
7 x 7 = 49 |
12 |
12 x 12 = 144 |
49 + 144 = 193 (✓) |
Length of the smaller unshaded square = 7 m
Length of the bigger unshaded square = 12 m
Total areas of the shaded right-angled triangles
= 12 x 7
= 84 m
2 Answer(s): 84 m
2