Students must use their prior knowledge of area and perimeter involving two-dimensional shapes. Students will now apply the concept of scale factor which changes the side lengths of a two-dimensional shape, affecting the perimeter and area. Students need to understand that when an image is dilated the area of the new image is the the product of the area of the original figure and the scale factor squared. Students understand that a dilation with scale factor greater than 1 is an enlargement and a scale factor less than one is a reduction. Students should also understand that the scale factor from one image to another is the reciprocal if reversing the dilation.
Read the two problem situations below and justify your thinking for each solution.
1. The perimeter of the shape below is 36 inches.If a scale factor of ½ is applied to the shape, what would happen to the perimeter?
2. The area of the shape below is 36 inches.
If a scale factor of ½ is applied to the shape, what would happen to the area?Hints
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8.10 Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:
(D) model the effect on linear and area measurements of dilated two-dimensional shapes