Math With AmarA C A D E M Y

Grade 6 · Build base-times-height area · 361 of 750

Build base-times-height area · practice 36

Find the area of a rectangle with base 1 and perpendicular height 9. 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 area of a rectangle with base 1 and perpendicular height 9.

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
Build base-times-height area · practice 36. Base: 1. Perpendicular height: 9. Revealed area: 0. Final area: 9Area accumulates in equal-width stripsOriginal dimensions: 1 by 9Full area = 9 square unitsLength × perpendicular height
This drawing uses the rectangular special case of a parallelogram. Lengths are positive and use one common unit. The fill is a continuous area sweep, not a count of indivisible tiles.

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.

Base
1
Perpendicular height
9
Revealed area
0
Final area
9

HD animation studio

From experiment to screen.

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The mathematical idea

Area counts square units covering a region. A rectangle's rows each have length b and its perpendicular height tells how many such rows fit. A parallelogram with the same base and perpendicular height has the same area after cutting and rearranging. Starting quantities: Base length = 1; Perpendicular height = 9.

A = base × perpendicular height

03 · Reflect and transfer

Explain what changes and why.

What happens to the area if only the perpendicular height doubles?

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.