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# Lesson 16 — Activity 2: Constructing Rectangles When Given the Area

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Lesson 16 — Activity 2: Constructing Rectangles when given the Area

#### Getting Ready

#### Sometimes you are only given the area of a shape and are asked to figure out what the shape looks like. In this activity, you will learn how to create a rectangle when you are given the area. In all of the rectangles you build, all units will be whole numbers.

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Let's start out with a rectangle that is 16 units^{2}. You know that a rectangle consists of two equal lengths and two equal widths.

The easiest way to create all of the possible shapes for this rectangle is to start with the smallest possible width which is 1 unit and work your way up through different widths.

If you know the area and have chosen a width, all you have to do is divide the area by the width to find the length.

l = A ÷ w

l = 16 ÷ 1

l = 16 units

The length of the rectangle is 16 units.

Let's start out with a rectangle that is 16 units

The easiest way to create all of the possible shapes for this rectangle is to start with the smallest possible width which is 1 unit and work your way up through different widths.

If you know the area and have chosen a width, all you have to do is divide the area by the width to find the length.

^{2}. You know that a rectangle consists of two equal lengths and two equal widths.The easiest way to create all of the possible shapes for this rectangle is to start with the smallest possible width which is 1 unit and work your way up through different widths.

If you know the area and have chosen a width, all you have to do is divide the area by the width to find the length.

l = A ÷ w

l = 16 ÷ 1

l = 16 units

The length of the rectangle is 16 units.

l = 16 ÷ 1

l = 16 units

The length of the rectangle is 16 units.

#### Try This:

#### Make a width of 2 units.

####
l = 16 ÷ 2

l = 8 units

The length of the rectangle is 8 units.

#### What about a width of 3 units?

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l = 16 ÷ 3

####

l = 5.3333

#### Because we only want to work with sides that are whole numbers, we can't make this rectangle.

#### What about a width of 4 units?

l = 16 ÷ 4

l = 4

This will not work either because any shape that has equal sides is a square, and you are only creating rectangles.

Therefore, there are only two possible shapes for a rectangle with an area of 16 units^{2}. One has a length of 16 and a width of 1 and the other has a length of 8 and a width of 2.

#### Try this:

####
Find three possible lengths and widths for a rectangle with an area of 12 units^{2}. Use the formula above and start with 1 unit.

####
l = 12 ÷ 1

l = 12
units

The length of the rectangle is 12 units.

l = 12 ÷ 2

l = 6
units

The length of the rectangle is 6 units.

l = 12 ÷ 3

l = 4
units

The length of the rectangle is 4 units.