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Grade 3 · Perimeter

Festival lanterns: separate covering from boundary distance

A rectangular plan for a neighborhood festival measures 3 units across and 11 units high. Change the controls and explain what the animation reveals.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Festival lanterns: separate covering from boundary distance. Boundary traced: 0. Perimeter in length units: 28. Area in square units: 33Perimeter 28 · area 33311Boundary traced: 0 length units
The quantities are invented for this investigation. Controls change the model rather than real-world records. Displayed decimals are rounded; whole-number counts are exact.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Boundary traced
0
Perimeter in length units
28
Area in square units
33

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

A rectangular plan for a neighborhood festival measures 3 units across and 11 units high. Perimeter is the complete boundary distance. Opposite sides of a rectangle are equal, so add both widths and both heights. Area instead measures the interior covering. The full boundary is 28 length units, while the area is 33 square units. These quantities answer different questions.

A relationship to keep

P = 2(3 + 11) = 28; A = 33

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Read the starting situation

    A rectangular plan for a neighborhood festival measures 3 units across and 11 units high. Identify what each number measures before changing a control; the worked example refers to these starting values.

  2. STEP 2

    Follow the mathematical change

    Trace the boundary without jumping across the interior. Pause at a corner and identify which lengths have already been counted. Pause on an intermediate frame and compare the picture with the live readouts.

  3. STEP 3

    Explain and test the relationship

    The full boundary is 28 length units, while the area is 33 square units. These quantities answer different questions. Change one input, predict its effect, and test whether the same relationship still works.

Your turn to explain

Make a prediction. Test your reasoning.

Festival lanterns: use the original situation. A rectangular plan for a neighborhood festival measures 3 units across and 11 units high. Increase the width by one unit while keeping the height fixed. How much does the perimeter increase?

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

It increases by 2 units because both horizontal sides grow by one. The new perimeter is 30.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 3 · Geometry

Same perimeter, different area

Separate boundary length from covered area.