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 42 cm, and the total area of the two unshaded squares is 180 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 42 cm
2 lengths of big square + 2 lengths of small square + 2 x 3 = 42
2 lengths of big square + 2 lengths of small square + 6 = 42
2 lengths of big square + 2 lengths of small square = 42 - 6
2 x (1 length of big square + 1 length of small square) = 36
1 length of big square + 1 length of small square = 36 ÷ 2 = 18
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 18 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 |
13 |
13 x 13 = 169 |
25 +169 = 194 (X) |
7 |
7 x 7 = 49 |
11 |
11 x 11 = 121 |
49 + 121 = 170 (X) |
6 |
6 x 6 = 36 |
12 |
12 x 12 = 144 |
36 + 144 = 180 (✓) |
Length of the smaller unshaded square = 6 m
Length of the bigger unshaded square = 12 m
Total areas of the shaded right-angled triangles
= 12 x 6
= 72 m
2 Answer(s): 72 m
2