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 38 cm, and the total area of the two unshaded squares is 146 cm
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 38 cm
2 lengths of big square + 2 lengths of small square + 2 x 3 = 38
2 lengths of big square + 2 lengths of small square + 6 = 38
2 lengths of big square + 2 lengths of small square = 38 - 6
2 x (1 length of big square + 1 length of small square) = 32
1 length of big square + 1 length of small square = 32 ÷ 2 = 16
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 16 cm.
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 |
4 |
4 x 4 = 16 |
12 |
12 x 12 = 144 |
16 +144 = 160 (X) |
6 |
6 x 6 = 36 |
10 |
10 x 10 = 100 |
36 + 100 = 136 (X) |
5 |
5 x 5 = 25 |
11 |
11 x 11 = 121 |
25 + 121 = 146 (✓) |
Length of the smaller unshaded square = 5 cm
Length of the bigger unshaded square = 11 cm
Total areas of the shaded right-angled triangles
= 11 x 5
= 55 cm
2 Answer(s): 55 cm
2