Question

These figures are similar. The perimeter and

area of one are given. The perimeter of the
other is also given. Find its area and round
to the nearest tenth.
Perimeter = 20 cm
Area = 18.6 cm?
Perimeter = 28 cm
Area = [? ]cm​

Answer 1

36.5 cm²

Step-by-step 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:

`(2k(l+w))/(2(l+w)) =(28)/(20) \\k=1.4`

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