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The area of Shape A is 12. Shape B is similar to Shape A and has a scale factor of 3. What is the area of Shape B?

Mathematics

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Step-by-step solution

3 steps

Here's how to solve the problem:

  1. Understand the relationship between the areas of two similar shapes and the scale factor.

    If a shape is enlarged by a scale factor kk, its area is enlarged by a factor of k2k^2.
    The formula is:

    Area of new shape=Area of original shape×(Scale Factor)2\text{Area of new shape} = \text{Area of original shape} \times (\text{Scale Factor})^2

  2. Identify the given values from the problem.

    The scale factor (kk) is 3.
    The area of Shape A (original shape) is 12.

  3. Calculate the area of Shape B (new shape).

    Substitute the values into the formula:

    Area of B=12×(3)2\text{Area of B} = 12 \times (3)^2 Area of B=12×9\text{Area of B} = 12 \times 9 Area of B=108\text{Area of B} = 108

    The area of Shape B is 108\boxed{108}.

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