Lesson 6: Practice Problems

Problem 1

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

A polygon aligned to a square grid is labeled Q. The shape is composed of 3 rectangles. The left part of the shape is 2 squares tall and 1 square wide. The next part of the shape is 3 squares tall and 2 squares wide. The next part of the shape begins 1 square up from the bottom of the shape and is 2 squares tall by 4 squares wide.

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)

Problem 3

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

A polygon aligned to a square grid labeled Q. The polygon is made up of 4 shapes, joined together along their edges. On the left is a right triangle with a base of 1 unit and a height of 2 units. To the right of the triangle is a 2 unit by 1 unit rectangle aligned with its 2 unit side next to the 2 unit side of the triangle. To the right of this is a 1 unit square, on top of a one-half unit triangle.

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

Problem 4 From Unit 1 Lesson 2

Here is an unlabeled polygon, along with its scaled copies Polygons –. 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. The unlabeled polygon has 4 sides, with a vertical heightof 2 on the left side. The height of the vertical side in each polygon is as follows: Polygon A: 1 unit. Polygon B: 4 units. Polygon C: 3 units. Polygon D: 2 units.

Problem 5 From Unit 1 Lesson 5

Solve each equation mentally.