Question

Use the scale factor to find the area of the enlarged figure. Explain your steps.

A small rectangle has a length of 8 and width of 4. A large rectangle has a length of 25.6 and width of a.

Answer 1

The scale factor of the enlargement is 3.2. Square the scale factor to get 10.24. Find the area of the original figure, which is 32. Multiply 32 and 10.24 to get the area of the enlarged figure, which is 327.68.

Explanation:

This is the sample response but I would use the other pearsons answer because it is NOT the sample response.

Have a great day!

Answer 2

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Answer:

327.68 units^2

Explanation:

The area of the small figure is ...

area = length · width

area = (8)(4) = 32 . . . . square units

The scale factor is ...

scale factor = large length / small length = 25.6/8 = 3.2

The area of the larger rectangle will be the small rectangle area multiplied by the square of the scale factor:

(32 units^2)(3.2^2) = 327.68 units^2

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Additional comment

We note the width is half the length, so we could figure the larger rectangle's width at 25.6/2 = 12.8 units. Then its area would be

length · width = (25.6 units)(12.8 units) = 327.68 units^2

This seems easier to me, but is not the method required by the problem statement.