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:
![\frac{2k(l+w)}{2(l+w)} =\frac{28}{20} \\k=1.4](https://tex.z-dn.net/?f=%5Cfrac%7B2k%28l%2Bw%29%7D%7B2%28l%2Bw%29%7D%20%3D%5Cfrac%7B28%7D%7B20%7D%20%5C%5Ck%3D1.4)
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
Answer:
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