棱镜公式
棱镜可以定义为一个多面体，它有两个彼此相对的多边形底面和一些侧面。棱镜具有折射光线的光滑抛光表面。棱镜的底面通常为三角形，侧面为矩形或平行四边形。
棱镜的特性
- 棱柱的两个底面相互平行，形状大多为三角形。
- 底面（底面和顶面）以外的面称为侧面。
- 棱镜具有折射光的特性。
- 通过在特定角度使用棱镜，白光可以分成七种彩虹色。
- 侧面为平行四边形或矩形。
棱镜公式
Surface area of Prism = (2×BaseArea) + Surface Area of Lateral Surfaces
棱镜类型
有不同类型的棱镜：
三棱镜
它是最简单的棱镜类型，有两个三角形面，可称为底面和顶面，三个侧面为矩形。
Area of base = 1/2 × (base) × (height) = 1/2 × (b) × (h)
Total Surface Area = Area of two bases + Area of 3 lateral surfaces
= 2 × (1/2×(base)×(height)) + 3 × length×breadth
= b × h + 3 × a × b
矩形棱镜
它是一种棱镜，有两个矩形面，可称为底面和顶面，四个侧面呈矩形。它看起来像一个长方体。
Area of base = (breadth) × (height)
Total Surface Area = Area of two bases + Area of 4 lateral surfaces
= 2×(breadth)×(height) + 2×length×breadth + 2×length×height
五棱镜
它是一种棱柱，有两个五边形面，可称为底面和顶面，五个侧面呈矩形。
Area of base = 5/2×a×b
Total Surface Area = Area of two bases + Area of 5 lateral surfaces
= 2×(5/2×a×b) + 5×b×h
= (5×a×b) + 5×b×h
六角棱镜
它是一种棱柱，有两个六边形面，可称为底面和顶面，六个侧面为矩形。
Area of base = 3×a×b
Total Surface Area = Area of two bases + Area of 6 lateral surfaces
= 2×(3×a×b) + 6×b×h
= (6×a×b) + 6×b×h
示例问题
问题1：求长10厘米、宽6厘米、高2厘米的三棱柱的面积。
解决方案：
Given length (a) = 10 cm, breadth (b) = 6 cm, and height (h) = 2 cm.
Area of triangular prism
Total Surface Area = Area of two bases + Area of 3 lateral surfaces
= 2×(1/2×(base)×(height)) + 3×length×breadth
= b×h + 3×a×b
= 6×2 + 3×10×6
= 12 + 180
= 192 cm2
问题2：求长10厘米、宽6厘米、高2厘米的长方体的面积。
解决方案：
Given length (a) = 10 cm, breadth (b) = 6 cm, and height (h) = 2 cm.
Area of the rectangular prism
Total Surface Area = Area of two bases + Area of 4 lateral surfaces
= 2×(breadth)×(height) + 2×length×breadth + 2×length×height
= 2×6×2 + 2×10×6 + 2×10×2
= 24 + 120 + 40
= 184 cm2
问题 3：求五棱柱的面积，其 a = 5 cm，宽 6 cm，高 10 cm。
解决方案：
Given (a) = 5 cm, breadth (b) = 6 cm, and height (h) = 10 cm.
Area of a pentagonal prism
Total Surface Area = Area of two bases + Area of 5 lateral surfaces
= 2×(5/2×a×b) + 5×b×h
= (5×a×b) + 5×b×h
= (5×5×6) + 5×6×10
= 150 + 300
= 450 cm2
问题4：求a=5cm、宽6cm、高10cm的六棱柱面积。
解决方案：
Given (a) = 5 cm, breadth (b) = 6 cm, and height (h) = 10 cm.
Area of a hexagonal prism
Total Surface Area = Area of two bases + Area of 6 lateral surfaces
= 2×(3×a×b) + 6×b×h
= (6×a×b) + 6×b×h
= (6×5×6) + 6×6×10
= 180 + 360
= 540 cm2
问题 5：求宽 6 厘米高 10 厘米的六棱柱的侧面面积。
解决方案：
Given breadth (b) = 6 cm, and height (h) = 10 cm.
Area of 6 lateral surfaces = 6×b×h
= 6×6×10
= 360 cm2