Math With AmarA C A D E M Y

Grade 7 · Account for every box face · 598 of 750

Account for every box face · practice 64

Find the surface area of a closed rectangular box with edge lengths 4.5, 6, and 6. Follow the calculation, then test the quantities in the animated example.

Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.

01 · Make a prediction

Your practice question

Find the surface area of a closed rectangular box with edge lengths 4.5, 6, and 6.

Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.

02 · Explore the model

See the mathematical relationship move.

Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.

Watch the relationship

Paused
Account for every box face · practice 64. Faces highlighted: 1. One ab face: 27. One ac face: 27. All six faces: square units: 180Six outside faces · a schematic net4.5 × 6ab = 274.5 × 6ac = 276 × 6bc = 364.5 × 6ab = 274.5 × 6ac = 276 × 6bc = 36All faces: 180 square units
All six faces are included; this is a closed box with negligible thickness. The net is schematic and each face has its own fit-to-cell scale, so read dimensions and area labels rather than comparing displayed areas.

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.

Faces highlighted
1
One ab face
27
One ac face
27
All six faces: square units
180

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.

The mathematical idea

Surface area adds the areas of the outside faces rather than measuring the space inside a box. A rectangular prism has three different face products, each appearing twice. A net exposes all six rectangles so hidden faces are not forgotten. Starting quantities: Length = 4.5; Width = 6; Height = 6.

S = 2(ab + ac + bc)

03 · Reflect and transfer

Explain what changes and why.

Which area would you subtract if the box had no top?

This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.