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Grade 10 · Area

Science exhibit: Compare a triangle's base and altitude

Science exhibit investigation: compare a triangle's base and altitude. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.

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

Watch the relationship

Paused
Science exhibit: Compare a triangle's base and altitude. Base: 4.5. Perpendicular height: 2. Revealed area: 0. Final area: 4.5A triangle occupies half its rectangleOriginal dimensions: 4.5 by 2Full area = 4.5 square unitsBase and height meet at a right angle.
The displayed triangle is right-angled, while the base-height area rule also applies to other triangles. Positive lengths share the same unit. A similar inset triangle reveals a chosen area fraction, not a constant-speed height sweep.

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
4.5
Perpendicular height
2
Revealed area
0
Final area
4.5

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 triangle with a horizontal base occupies half of the rectangle sharing that base and perpendicular height. Pairing it with a congruent triangle explains the factor one half. Slanted edge length cannot replace perpendicular height in the formula. This investigation begins with base length = 4.5; perpendicular height = 2. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

A = base × perpendicular height / 2

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

  1. STEP 1

    Represent the given quantities

    Read the horizontal base and the dashed perpendicular height, which meet at a right angle.

  2. STEP 2

    Follow the changing model

    Playback reveals corresponding fractions of the triangle and its matching rectangle. The triangle has exactly half the rectangle's area.

  3. STEP 3

    Check and explain the relationship

    Calculate both areas and compare them; changing either dimension scales both in the same proportion.

Your turn to explain

Make a prediction. Test your reasoning.

Science exhibit: Find the triangle area with base 4.5 and perpendicular height 2.

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

Compare your explanation

4.5 square units, half of the matching rectangle's 9.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 10 · Trigonometry

Find area without a stated altitude

Express a triangle's height using sine of the included angle.