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 m^2

perimeter = 34 m
area = ? m^2

Explanation:

Identify the relationship between similar figures

Using the Similarity Transformations knowledge point

$$ k = \frac{P_2}{P_1} = \frac{34}{20} = 1.7 $$

Relate the area ratio to the scale factor

Using the Similarity Transformations knowledge point

$$ \frac{A_2}{A_1} = k^2 = (1.7)^2 = 2.89 $$

Calculate the unknown area

Using the Similarity Transformations knowledge point

$$ A_2 = 19.6 \times 2.89 = 56.644\text{ m}^2 $$

Round to the nearest tenth

Using the Similarity Transformations knowledge point

$$ A_2 \approx 56.6\text{ m}^2 $$

Answer:

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 = \(20\text{ m}\)
Area = \(19.6\text{ m}^2\)

Perimeter = \(34\text{ m}\)
Area = <blank>\(56.6\)</blank> \(\text{m}^2\)