# 3.7 Two-dimensional Shapes and Perimeter

## Unit Goals

• Students reason about shapes and their attributes, with a focus on quadrilaterals. They solve problems involving the perimeter and area of shapes.

### Section A Goals

• Reason about shapes and their attributes.

### Section B Goals

• Find the perimeter of two-dimensional shapes, including when all or some side lengths are given.

### Section C Goals

• Solve problems involving perimeter and area, in and out of context.

### Section D Goals

• Apply geometric understanding to solve problems.

### Problem 1

#### Pre-unit

Practicing Standards:  2.G.A.1

1. Which shapes are hexagons? ____________________

2. Draw a quadrilateral and label it Q. Draw a pentagon and label it P.

### Problem 2

#### Pre-unit

Practicing Standards:  3.MD.C.7

1. Finish covering the rectangle with equal-sized squares.
2. Write an addition equation showing how many small squares there are in the rectangle.
3. Write a multiplication equation showing how many small squares there are in the rectangle.

### Problem 3

#### Pre-unit

Practicing Standards:  3.MD.C.7.d

What is the area of the figure?

### Problem 4

#### Pre-unit

Practicing Standards:  2.MD.A.1

Find the length of each rectangle.

### Problem 5

1. Which shapes have 5 angles? ____________________

2. Which shapes have all side lengths the same size? ____________________

### Problem 6

1. Which triangles have one right angle? ____________________

2. Which triangles have two sides that are the same length? ____________________

### Problem 8

Select all of the quadrilaterals that are rectangles.

### Problem 9

1. Draw a quadrilateral that is not a rhombus and label it A. Explain why your shape is not a rhombus.
2. Draw a quadrilateral that is not a rectangle and label it B. Explain why your shape is not a rectangle.

### Problem 10

#### Exploration

Find one of each of the following shapes in the image.

1. A triangle with a right angle
2. A triangle with 3 equal sides
3. A rhombus
4. A rectangle
5. A square

### Problem 11

#### Exploration

Do any of the triangles have:

1. a right angle?
2. two equal sides?
3. three equal sides?

### Problem 1

Find the perimeter of each shape.

### Problem 2

1. Draw 2 different shapes with perimeter 20 units.

2. What strategy did you use to draw your shapes?

### Problem 3

Find the perimeter of each shape. Explain or show your reasoning.

1.

2.

### Problem 4

All sides of this hexagon have the same length. The perimeter of the hexagon is 96 cm. What are its side lengths? Explain or show your reasoning.

### Problem 5

#### Exploration

The side length of every pattern block is 1 inch.

1. What is the perimeter of the shape? Explain your reasoning.
2. What is the perimeter of the shape if you remove the skinny rhombuses around the boundary?
3. What is the perimeter if you next remove the blue rhombuses? What if you keep removing more shapes?

### Problem 6

#### Exploration

1. Draw some different shapes that you can find the perimeter of. Then find their perimeters.
2. Can you draw a rectangle whose perimeter is odd? Explain or show your reasoning.
3. Can you draw a pentagon or hexagon (or a figure with even more sides) whose perimeter is odd?

### Problem 1

A rectangular card has an area of 60 square centimeters. It is 4 centimeters longer than it is wide. What is the perimeter of the card? Explain or show your reasoning.

### Problem 2

Draw two rectangles with perimeter 20 units on the grid whose areas are different. What are the areas of the rectangles?

### Problem 3

Draw two rectangles on the grid with area 30 square units whose perimeters are different. What are the perimeters of your rectangles?

### Problem 4

#### Exploration

Clare draws a rectangle.

1. She tells you that the perimeter is 36. What rectangle could Clare have drawn?
2. Then she tells you that her rectangle has the biggest area possible. What rectangle could Clare have drawn?

### Problem 5

#### Exploration

Draw a rectangle on the grid but don’t share with your partner. Give your partner clues to help them guess the perimeter and area of your rectangle. Try not to just tell them the side lengths of your rectangle.

### Problem 1

The perimeter of a rectangular park is 444 meters. The park is 175 meters long. How wide is the park? Explain or show your reasoning.

### Problem 2

1. Where do you see rhombuses in the design?
2. Where do you see rectangles in the design?
3. Are there any triangles in the design?

### Problem 3

1. The body of your robot has a perimeter of 64 units. What were some different lengths and widths you could choose that fit on the grid?
2. The head has a perimeter of 36 units. What were some different lengths and widths you could choose for the head that fit on the grid?

### Problem 4

#### Exploration

Han is making a rectangular garden in his backyard. He has 42 feet of fencing and the garden needs to be at least 3 feet wide. What are the possible lengths and widths of the garden Han could make? Explain or show your reasoning.