Lesson 6

Scaling and Area

Let's build scaled shapes and investigate their areas.

Problem 1

On the grid, draw a scaled copy of Polygon Q using a scale factor of 2. Compare the perimeter and area of the new polygon to those of Q.

A polygon aligned to a square grid is labeled Q

Problem 2

A right triangle has an area of 36 square units.

If you draw scaled copies of this triangle using the scale factors in the table, what will the areas of these scaled copies be? Explain or show your reasoning.

scale factor area (units2)
1 36

Problem 3

Diego drew a scaled version of a Polygon P and labeled it Q.

A polygon aligned to a square grid labeled Q.

If the area of Polygon P is 72 square units, what scale factor did Diego use to go from P to Q? Explain your reasoning.

Problem 4

Here is an unlabeled polygon, along with its scaled copies Polygons A–D. For each copy, determine the scale factor. Explain how you know.

An unlabeled four sided polygon with four different scale copies labeled A, B, C and D on a square grid. 
(From Unit 1, Lesson 2.)

Problem 5

Solve each equation mentally.

  1. \(\frac17\boldcdot x=1\)
  2. \(x \boldcdot \frac{1}{11}=1\)
  3. \(1\div \frac{1}{5}=x\)
(From Unit 1, Lesson 5.)