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 58 cm, and the total area of the two unshaded squares is 338 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 58 cm
2 lengths of big square + 2 lengths of small square + 2 x 5 = 58
2 lengths of big square + 2 lengths of small square + 10 = 58
2 lengths of big square + 2 lengths of small square = 58 - 10
2 x (1 length of big square + 1 length of small square) = 48
1 length of big square + 1 length of small square = 48 ÷ 2 = 24
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 24 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 |
6 |
6 x 6 = 36 |
18 |
18 x 18 = 324 |
36 +324 = 360 (X) |
8 |
8 x 8 = 64 |
16 |
16 x 16 = 256 |
64 + 256 = 320 (X) |
7 |
7 x 7 = 49 |
17 |
17 x 17 = 289 |
49 + 289 = 338 (✓) |
Length of the smaller unshaded square = 7 m
Length of the bigger unshaded square = 17 m
Total areas of the shaded right-angled triangles
= 17 x 7
= 119 m
2 Answer(s): 119 m
2