Question

i \can\ similarity
δabc ~ δdef with a proportion ratio of 1:3. what is the ratio of their areas?
a 1:3 c 1:6
b 1:9 d 2:9
37

Explanation:

Step1: Recall the area ratio formula for similar triangles

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. If the proportion ratio of the side lengths of \(\triangle ABC\) and \(\triangle DEF\) is \(k=\frac{1}{3}\), then the ratio of their areas \(k_{area}=k^{2}\).

Step2: Calculate the area ratio

Substitute \(k = \frac{1}{3}\) into the formula \(k_{area}=k^{2}\). We get \(k_{area}=(\frac{1}{3})^{2}=\frac{1}{9}\).

Answer:

B. \(1:9\)