Unit 1 · Essential SkillsE5 · Area Essentials · Ground Ops

Area, Perimeter & Volume Essentials

Choose the measurement the question asks for and combine familiar shapes efficiently.

29 min
Unlocks: Assembly Hangar
Desmos way

Ready when you are

7 steps · about 29 minutes

Start with the warm-up.

Start

Step 1 of 7Warm-upDone

Warm-up

Finish the previous step to continue, or use “Show everything” above to explore.

Key terms

Perimeter: Distance around a figure.
Area: Amount of two-dimensional surface.
Volume: Amount of three-dimensional space.

Step 2 of 7Try it firstDone

Try it first

Finish the previous step to continue, or use “Show everything” above to explore.

Take a shot before the lesson. Write one relationship from the stem, even if you do not finish.

Step 3 of 7LearnDone

The big idea

Finish the previous step to continue, or use “Show everything” above to explore.

See the structure

Perimeter measures boundary, area measures surface, and volume measures space. Identify the requested dimension before choosing a formula.

Key idea

Name quantities before calculating

Write what each number measures. A correct calculation with the wrong quantity or unit still misses the question.

Build a reliable method

Composite figures become easier when you add simple pieces or subtract a cutout from a larger shape. Mark overlaps so you do not count them twice.

Explore in Desmos

Match dimension to formula

A 9-by-7 floor has perimeter 32 units and area 63 square units. Giving it height 4 makes a rectangular prism with volume 252 cubic units. Read all three outputs and match each to boundary, surface, or space.

The calculator is live: change anything and see what happens.

Match dimension to formula

Degree mode

Loading Desmos…

Stretch to a 36

When every length scales by $k$ , perimeter scales by $k$ , area by $k^2$ , and volume by $k^3$ .

Trap

A believable answer to the wrong question

The choices often include a correct intermediate number. Before selecting it, reread the highlighted ask and check the unit, sign, and domain.

Step 4 of 7Worked examplesDone

Worked examples

Finish the previous step to continue, or use “Show everything” above to explore.

Skip check · 2 questions

Already know this? Get both right on the first try and you can skip the worked examples.

Worked example

Example 1: Match the formula to what is covered

Problem

A 9-by-4 floor is tiled. How many square units are covered?

Area counts unit squares:

A=9(4)

Which formula matches the requested dimension?

A=36

square units.

Which statement checks both the number and its units?

Worked example

Example 2: Build volume from three dimensions

Problem

A storage bin is 12 units long, 8 units wide, and 3 units high. What is its volume?

The

12\times8

base contains

96

unit squares. The height stacks 3 identical layers.

Which formula matches the requested dimension?

V=288

cubic units.

Which statement checks both the number and its units?

Faded example · you finish it

Example 3: Complete the setup and result

Problem

What area remains after a 2-by-2 corner is removed from a 10-by-6 rectangle?

Choose the setup that follows the stated relationship.

Choose the resulting value.

Desmos way

Subtract a cutout area, not a side length

For a 10-by-6 rectangle with a 2-by-2 corner removed, type 10*6 and 2^2. Read 60 square units for the whole and 4 for the cutout.

Type 10*6-2^2 and read 56 square units. The exponent matters because the removed measurement is an area, not a length.

Subtract a cutout area, not a side length

Degree mode

Loading Desmos…

Step 5 of 7PracticeDone

Practice

Finish the previous step to continue, or use “Show everything” above to explore.

Step 6 of 7Spot the mistakeDone

Spot the mistake

Finish the previous step to continue, or use “Show everything” above to explore.

Spot the mistake

Where did it go wrong?

One line has an error. Click the line where it first goes wrong.

Step 7 of 7Exit ticketDone

Exit ticket

Finish the previous step to continue, or use “Show everything” above to explore.

Optional · 4 questions · Hardest levelChallenge set: the kind of question that decides a 36

These are last-ten-questions hard. Take your time, use Desmos when it helps, and expect to miss some: that's where the learning is.