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 60 cm, and the total area of the two unshaded squares is 306 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 60 cm
2 lengths of big square + 2 lengths of small square + 2 x 6 = 60
2 lengths of big square + 2 lengths of small square + 12 = 60
2 lengths of big square + 2 lengths of small square = 60 - 12
2 x (1 length of big square + 1 length of small square) = 48
1 length of big square + 1 length of small square = 48 ÷ 2 = 24
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 24 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 |
8 |
8 x 8 = 64 |
16 |
16 x 16 = 256 |
64 +256 = 320 (X) |
10 |
10 x 10 = 100 |
14 |
14 x 14 = 196 |
100 + 196 = 296 (X) |
9 |
9 x 9 = 81 |
15 |
15 x 15 = 225 |
81 + 225 = 306 (✓) |
Length of the smaller unshaded square = 9 m
Length of the bigger unshaded square = 15 m
Total areas of the shaded right-angled triangles
= 15 x 9
= 135 m
2 Answer(s): 135 m
2