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 36 cm, and the total area of the two unshaded squares is 117 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 36 cm
2 lengths of big square + 2 lengths of small square + 2 x 3 = 36
2 lengths of big square + 2 lengths of small square + 6 = 36
2 lengths of big square + 2 lengths of small square = 36 - 6
2 x (1 length of big square + 1 length of small square) = 30
1 length of big square + 1 length of small square = 30 ÷ 2 = 15
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 15 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 |
5 |
5 x 5 = 25 |
10 |
10 x 10 = 100 |
25 +100 = 125 (X) |
7 |
7 x 7 = 49 |
8 |
8 x 8 = 64 |
49 + 64 = 113 (X) |
6 |
6 x 6 = 36 |
9 |
9 x 9 = 81 |
36 + 81 = 117 (✓) |
Length of the smaller unshaded square = 6 m
Length of the bigger unshaded square = 9 m
Total areas of the shaded right-angled triangles
= 9 x 6
= 54 m
2 Answer(s): 54 m
2