LEARN · EXPLAIN · REVISE

A horizontal rectangle has side lengths 2 and 4. Its receding side is drawn at half length and 45°. The drawn area is c√2. Find c.

Read the idea, work independently, then explain what changed.

高一必修第二册(A版).pdf · 8.2 · PDF 114 / printed page 107

TOPIC 01

Oblique drawings of solids

Build understanding of oblique drawings of solids through definitions, contrasting cases and justified applications.

Use definitions, valid spatial reasoning and metric checks for oblique drawings of solids.
Connect representations and justify the steps, including boundary cases.
Explain a solution and apply the idea to a changed situation.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Distinguish the actual spatial object from the stated oblique drawing convention.

Hint 2

Multiply adjacent drawn lengths by sine of the drawn angle.

Worked solution

Distinguish the actual spatial object from the stated oblique drawing convention.
Calculate or simplify this relation.
$S_{\text{draw}}=2\cdot(4/2)\cdot\sin45^{\circ}=2\sqrt2$
The drawing area differs from the actual base area.

The requested value is 2.

Checks and common pitfalls: The drawing area differs from the actual base area.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Use definitions, valid spatial reasoning and metric checks for oblique drawings of solids.
Drawing convention: The common 45° oblique convention halves receding lengths while retaining other stated scales.
Representation limits: A sketch preserves selected incidence and parallel relations, but not all angles or distances.
Close with: conditions → representation → reasoning → check.

Expected reasoning: The common 45° oblique convention halves receding lengths while retaining other stated scales.
Expected reasoning: A sketch preserves selected incidence and parallel relations, but not all angles or distances.
Expected correction: A measured sketch length need not equal a true spatial length.