Chapter 9

Perimeter, Area and Volume

Measuring the edge, the surface and the space inside — with units that make it obvious when the wrong formula has been used.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Geometry and Measure)ตรงกับเนื้อหาการวัดใน ม.1 และต่อไปยัง ม.2 บทที่ 3 ปริซึมและทรงกระบอก
Common Core (US): 6.G, 7.G
Cambridge: Lower Secondary Stage 7 — Geometry and Measure: shapes and measurements

9.1 Perimeter and area

นิยาม

Perimeter and area

Perimeter is the distance all the way round, measured in cm or m. Area is the amount of surface covered, measured in cm² or m². They answer different questions and carry different units.

The formulae for this stage

A_{rectangle} = l w A_{triangle} = \frac{1}{2} bh A_{parallelogram} = bh

In every one of these, $h$ is the PERPENDICULAR height — not the slanted side.

ข้อควรระวัง

The slant length is offered in almost every triangle question precisely because it is the wrong number. The height must be at right angles to the base you are using.

Compound shapes

1Split the shape into rectangles and triangles
2Find any missing lengths by subtracting the ones you have
3Work out each piece separately and add
4Alternatively, take a whole rectangle and subtract the missing corner

ตัวอย่าง

An L-shape is made from a $10 \times 6$ rectangle with a $4 \times 3$ rectangle removed from one corner. Find its area.

วิธีทำ

1.Whole rectangle: $10 \times 6 = 60$ cm²
2.Removed piece: $4 \times 3 = 12$ cm²
3. $60 - 12$

ตอบ $48$ cm²

ทำไมถึงเป็นแบบนั้น

A triangle is half a parallelogram with the same base and height — two copies of it fit together to make one. That is where the $\frac{1}{2}$ comes from, and remembering the picture is more reliable than remembering the formula.

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