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 m area = 19.6 m² perimeter = 34 m area = ? m²

Explanation:

Step1: Find the ratio of perimeters

The ratio of perimeters \( r=\frac{34}{20} = 1.7\)

Step2: Use the ratio of areas formula

For similar figures, if the ratio of perimeters is \(r\), the ratio of areas is \(r^{2}\). Let the unknown area be \(A\). We know that \(\frac{A}{19.6}=r^{2}\). Substitute \(r = 1.7\) into the formula: \(A=19.6\times(1.7)^{2}\)

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Answer:

\(56.6\space m^{2}\)