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 72 cm, and the total area of the two unshaded squares is 522 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 72 cm
2 lengths of big square + 2 lengths of small square + 2 x 6 = 72
2 lengths of big square + 2 lengths of small square + 12 = 72
2 lengths of big square + 2 lengths of small square = 72 - 12
2 x (1 length of big square + 1 length of small square) = 60
1 length of big square + 1 length of small square = 60 ÷ 2 = 30
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 30 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 |
22 |
22 x 22 = 484 |
64 +484 = 548 (X) |
10 |
10 x 10 = 100 |
20 |
20 x 20 = 400 |
100 + 400 = 500 (X) |
9 |
9 x 9 = 81 |
21 |
21 x 21 = 441 |
81 + 441 = 522 (✓) |
Length of the smaller unshaded square = 9 m
Length of the bigger unshaded square = 21 m
Total areas of the shaded right-angled triangles
= 21 x 9
= 189 m
2 Answer(s): 189 m
2