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 34 cm, and the total area of the two unshaded squares is 116 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 34 cm
2 lengths of big square + 2 lengths of small square + 2 x 3 = 34
2 lengths of big square + 2 lengths of small square + 6 = 34
2 lengths of big square + 2 lengths of small square = 34 - 6
2 x (1 length of big square + 1 length of small square) = 28
1 length of big square + 1 length of small square = 28 ÷ 2 = 14
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 14 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 |
11 |
11 x 11 = 121 |
9 +121 = 130 (X) |
5 |
5 x 5 = 25 |
9 |
9 x 9 = 81 |
25 + 81 = 106 (X) |
4 |
4 x 4 = 16 |
10 |
10 x 10 = 100 |
16 + 100 = 116 (✓) |
Length of the smaller unshaded square = 4 m
Length of the bigger unshaded square = 10 m
Total areas of the shaded right-angled triangles
= 10 x 4
= 40 m
2 Answer(s): 40 m
2