Perimeter, area and volume

边玩边学

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课程笔记

Perimeter is the distance around a shape; area is the space inside.
Rectangle: A = lw. Triangle: A = \frac{1}{2}bh. Parallelogram: A = bh. Trapezium: A = \frac{1}{2}(a + b)h.
Circle: circumference C = 2\π r = \π d; area A = \π r².
For compound shapes, split into simple parts and add or subtract.
Use perpendicular height for triangle, parallelogram and trapezium area. Perimeter adds all outside edges; include straight edges when finding a semicircle’s perimeter.

Prism: volume = cross-sectional area × length. Cuboid: V = lwh. Cylinder: V = \π r² h; curved surface area 2\π rh.
Cone: V = \frac{1}{3}\π r² h; curved surface area \π r l (slant height l).
Sphere: V = \frac{4}{3}\π r³; surface area 4\π r². Pyramid: V = \frac{1}{3} \times \text{base area} \times h.
For a closed cylinder, add both circular ends: total surface area = 2πr² + 2πrh. A right cone has total surface area πr² + πrl, with slant height l; an open solid omits its missing faces.
Cylinder and cone formulas here refer to right circular solids. The h in each volume formula is perpendicular height.

Length: cm, m. Area: cm², m². Volume: cm³, m³. 1 m² = 10 000 cm²; 1 m³ = 1 000 000 cm³; 1 litre = 1000 cm³.
Always state the correct units.

Draw and label diagrams, identify the shape, pick the formula, and substitute carefully, giving the answer in an appropriate form (in terms of \π or to 3 s.f.).

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