Question

a garden has an area of 400 square meters. you need to create a scale model with a scale factor of 1:10. what is the area of the model in square meters? use the keypad to enter your answer in the box. the area of the model is square meters.

Explanation:

Step1: Recall the relationship between scale factor and area

If the scale factor of two similar figures is \(a:b\), the ratio of their areas is \(a^{2}:b^{2}\). Here, the scale factor of the model to the garden is \(1:10\), so the ratio of the area of the model to the area of the garden is \(1^{2}:10^{2}=1:100\).

Step2: Set up a proportion to find the area of the model

Let \(x\) be the area of the model. We have the proportion \(\frac{x}{400}=\frac{1}{100}\). Cross - multiply gives \(100x = 400\).

Step3: Solve for \(x\)

Divide both sides of the equation \(100x = 400\) by \(100\). So \(x=\frac{400}{100}=4\).

Answer:

4