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 28 cm, and the total area of the two unshaded squares is 65 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 28 cm
2 lengths of big square + 2 lengths of small square + 2 x 3 = 28
2 lengths of big square + 2 lengths of small square + 6 = 28
2 lengths of big square + 2 lengths of small square = 28 - 6
2 x (1 length of big square + 1 length of small square) = 22
1 length of big square + 1 length of small square = 22 ÷ 2 = 11
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 11 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 |
3 |
3 x 3 = 9 |
8 |
8 x 8 = 64 |
9 +64 = 73 (X) |
5 |
5 x 5 = 25 |
6 |
6 x 6 = 36 |
25 + 36 = 61 (X) |
4 |
4 x 4 = 16 |
7 |
7 x 7 = 49 |
16 + 49 = 65 (✓) |
Length of the smaller unshaded square = 4 m
Length of the bigger unshaded square = 7 m
Total areas of the shaded right-angled triangles
= 7 x 4
= 28 m
2 Answer(s): 28 m
2