Answer:
36.5 cm²
Explanation:
The perimeter of the smaller shape = 20 cm and The area of the smaller shape = 18.6 cm²
The perimeter of the bigger shape = 28 cm
The length and breadth of the smaller shape is increased by a factor of k to produce the larger shape.
If the length of the smaller shape = l and its width = w. The perimeter of the smaller shape = 2(l + w) = 20
Since The length and breadth of the smaller shape is increased by a factor of k to produce the larger shape, the length of the larger shape = kl and its width = kw. Therefore the perimeter of the larger shape = 2(kl + kw) = 2k (l + w) = 28 cm
To find k, divide the perimeter of the larger shape by the perimeter of the larger shape:
[tex]\frac{2k(l+w)}{2(l+w)} =\frac{28}{20} \\k=1.4[/tex]
The area of the smaller shape = l * w = 18.6 cm²
The area of the larger shape = kl * kw = k² * l * w = 1.4² * 18.6 cm² = 36.5 cm²
