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

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:

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

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