المساحات والمحيطات والأشكال المستوية المركبة · المستوى المتقدم
مُقدَّم| English | المعنى |
|---|---|
| perpendicular height/ˌpɜːpənˈdɪkjʊlə haɪt/ | الارتفاع العمودي |
A sloping garden fence can have a long side but a small perpendicular height. The side length and the height serve different jobs in an area formula.
- A sloping garden fence can have a long side but a small perpendicular height. The side length and the height serve different jobs in an area formula.
- This lesson studies perpendicular height 垂直高度: The distance between a base and its parallel opposite level, measured at right angles.
Choose the mathematical structure
- Triangle area is bh/2, parallelogram area bh and trapezium area (a+b)h/2 for parallel sides a,b. Heights are perpendicular to the selected base. Perimeter adds only the outside boundary. Split a composite shape into non-overlapping parts, or subtract a missing region from a containing shape.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
لماذا يجب أن يكون الارتفاع في A=bh/2 عمودياً على القاعدة؟
Difficulty 1/5 · 100 coins + a small bonus on first completion today
تقيس صيغة المساحة مدى امتداد الشكل عمودياً على قاعدته. استخدام الضلع المائل يُبالغ في الإجابة؛ فالمستطيل الزاوي المسطح جداً له مساحة صغيرة رغم أطوال أضلاعه المائلة.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
A triangle with base 8 cm and height 5 cm has area 20 cm²; a parallelogram with the same base/height has area 40 cm². A trapezium with parallel sides 6 and 10 cm and height 4 cm has area (6+10)×4/2=32 cm². A rectangular 8 by 6 cm sheet with a 3 by 2 cm corner removed has area 48-6=42 cm². Its perimeter is still 28 cm: the two removed outside segments total 5 cm and the two new notch edges also total 5 cm. This perimeter equality depends on a corner rectangular cut; an internal hole adds a separate boundary. Rearranging triangle area gives h=2A/b.
المساحات والمحيطات والأشكال المستوية المركبة
مساحة المثلث bh/2، ومساحة متوازي الأضلاع bh، ومساحة شبه المنحرف (a+b)h/2 للأضلاع المتوازية a,b
صنّف عبارات الحالة المحلولة، ثم اشرح الوحدات أو الثوابت التي تبرر كل قرار.
أوجد مساحة شبه المنحرف لأضلاع متوازية 6,10 وارتفاع 4.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
(6+10)×4/2=32.
Test a tempting shortcut
- Use perpendicular height rather than a sloping side. A shared internal division line is not part of the perimeter. An area answer has squared units; a perimeter answer has length units.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
The sloping side of a parallelogram is always its perpendicular height. This claim is false. Explain which definition or assumption it violates.
أوجد مساحة مستطيل 8×6 تم إزالة زاوية منه بحجم 3×2.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
8×6-3×2=42.
الضلع المائل في متوازي الأضلاع ليس هو ارتفاعه العمودي دائمًا.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
استخدم الارتفاع العمودي بدلاً من الضلع المائل. لا يُحسب خط التقسيم الداخلي المشترك ضمن المحيط. الإجابة عن المساحة تكون بوحدة مربعة، بينما الإجابة عن المحيط تكون بوحدة طول.
Interpret a new situation
- AQA G16/G17 includes triangle/parallelogram/trapezium area and composite perimeter/area. Mark the parallel bases, perpendicular height and counted outside edges before calculating.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
أوجد محيط الشكل الذي قطعت منه الزاوية.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
عد الحواف الخارجية الستة؛ فالقطع المثلثي يستبدل أطوالًا مساوية إجمالاً.
صل كل شكل بقانون مساحته.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
جميعها تستخدم الارتفاع العمودي؛ أما شبه المنحرف فيأخذ متوسط طولي ضلعَيه المتوازيين قبل الضرب.
Use this in your course
- 8300 · Higher · 3.4. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The distance between a base and its parallel opposite level, measured at right angles. Choose the relationship, show the method, check its assumptions and interpret the result.