Area, Circles and Volume

The trapezium, the circle, and the prisms built from them — with the one rule that makes every volume question at this stage the same question.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Geometry and Measure)ตรงกับ ม.2 บทที่ 3 ปริซึมและทรงกระบอก
Common Core (US): 7.G, 8.G
Cambridge: Lower Secondary Stage 8 — Geometry and Measure: shapes and measurements

9.1 Area of a trapezium and compound shapes

The area formulae for this stage

A_{triangle} = \frac{1}{2} bh A_{parallelogram} = bh A_{trapezium} = \frac{1}{2} (a + b) h

In every one, $h$ is the perpendicular height. In the trapezium, $a$ and $b$ are the two PARALLEL sides.

ทำไมถึงเป็นแบบนั้น

The trapezium formula is the average of the two parallel sides multiplied by the height. Two copies of the trapezium fit together into a parallelogram of base $a + b$ , which is where the halving comes from.

ตัวอย่าง

A trapezium has parallel sides $7$ cm and $11$ cm, and a perpendicular height of $6$ cm. Find its area.

วิธีทำ

1. $A = \frac{1}{2} (7 + 11) \times 6$
2. $= \frac{1}{2} \times 18 \times 6$

ตอบ $54$ cm²

ข้อควรระวัง

The slanted side of a trapezium is offered in almost every question and is never the height. Use only the distance measured at right angles between the two parallel sides.

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