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 62 cm, and the total area of the two unshaded squares is 388 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 62 cm
2 lengths of big square + 2 lengths of small square + 2 x 5 = 62
2 lengths of big square + 2 lengths of small square + 10 = 62
2 lengths of big square + 2 lengths of small square = 62 - 10
2 x (1 length of big square + 1 length of small square) = 52
1 length of big square + 1 length of small square = 52 ÷ 2 = 26
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 26 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 |
7 |
7 x 7 = 49 |
19 |
19 x 19 = 361 |
49 +361 = 410 (X) |
9 |
9 x 9 = 81 |
17 |
17 x 17 = 289 |
81 + 289 = 370 (X) |
8 |
8 x 8 = 64 |
18 |
18 x 18 = 324 |
64 + 324 = 388 (✓) |
Length of the smaller unshaded square = 8 m
Length of the bigger unshaded square = 18 m
Total areas of the shaded right-angled triangles
= 18 x 8
= 144 m
2 Answer(s): 144 m
2