Square a Linear Scale for Area - Practice 1

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If all linear dimensions are multiplied by k, area is multiplied by k squared. This model concerns geometrically similar shapes, not the distortions of arbitrary world projections. These are ideal rescaled local map patches.

Worked example

Enlarging both width and height by 3 gives 9 times the map area, not 3 times.

A small square is enlarged to a three-by-three grid of nine squares. Width and height each multiply by three, so the area multiplies by nine.

Question 1 Ideal map patch 1 starts with area 2 square cm. All lengths are enlarged by factor 2. What is its new area in square cm? Answer

Question 2 Ideal map patch 2 starts with area 3 square cm. All lengths are enlarged by factor 3. What is its new area in square cm? Answer

Question 3 Ideal map patch 3 starts with area 4 square cm. All lengths are enlarged by factor 4. What is its new area in square cm? Answer

Question 4 Ideal map patch 4 starts with area 5 square cm. All lengths are enlarged by factor 5. What is its new area in square cm? Answer

Question 5 Ideal map patch 5 starts with area 6 square cm. All lengths are enlarged by factor 2. What is its new area in square cm? Answer