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 52 cm, and the total area of the two unshaded squares is 233 m
2. Find the total area of the two shaded right-angled triangles.
Perimeter of the shaded area = 52 cm
2 lengths of big square + 2 lengths of small square + 2 x 5 = 52
2 lengths of big square + 2 lengths of small square + 10 = 52
2 lengths of big square + 2 lengths of small square = 52 - 10
2 x (1 length of big square + 1 length of small square) = 42
1 length of big square + 1 length of small square = 42 ÷ 2 = 21
Use guess and check.
Total length of the smaller unshaded square and bigger unshaded square must be 21 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 |
14 |
14 x 14 = 196 |
49 +196 = 245 (X) |
9 |
9 x 9 = 81 |
12 |
12 x 12 = 144 |
81 + 144 = 225 (X) |
8 |
8 x 8 = 64 |
13 |
13 x 13 = 169 |
64 + 169 = 233 (✓) |
Length of the smaller unshaded square = 8 m
Length of the bigger unshaded square = 13 m
Total areas of the shaded right-angled triangles
= 13 x 8
= 104 m
2 Answer(s): 104 m
2