棱锥的表面积可通过把所有侧面三角形面积和底面积相加得到。无论是什么形状都可以用这种方法来算。下面我们教你如何计算四棱锥、三棱锥、五棱锥和六棱锥的表面积。
步骤
方法 1 的 5:
常见四棱锥的计算公式
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1
要记住适用于所有棱锥的表面积公式。 计算任何棱锥时，用下列公式： SA = [(1/2) * p * h] + B
SA 表示 "surface area，表面积"。p 表示底面周长， h 是斜高， B 表示底面积。
可以通过把侧面积相加，即[(1/2) * p * h] ，然后加上底面积 B 得到总表面积。
侧面积可以看做所有侧面表面积之和。换句话说就是把所有侧面三角形面积相加。
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2
了解如何从基本公式中，得出四棱锥的表面积算法。 普通四棱锥的表面积就是SA = [2 * b * h] + b2
SA 、 h 和之前意义一样。
b 这个缩写代表棱锥的底边长。
[2 * b * h] 这个量是用来计算侧面积的。
1/2 * b * h 是一个侧面三角形面积。
4 * 1/2 2 * b * h 表示4个侧面三角形面积之和。4*1/2得到2*b*h。
正方形的面积是s2 ，这里的 s 表示一条边长。 s 在这里替换为 b 。
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3
确定三棱锥的公式。 大多数三棱锥可以用 SA = (1/2 * a * b) + (3/2 * b * h) 计算。
SA、 b'、 h 这里和前面一样。
a 代表边心距。
本公式中 (1/2 * a * b) 用来计算底面积， (3/2 * b * h) 用来计算侧面积。
标准三角形面积公式是(1/2 * a * b) ，但是标准棱锥中， a 就表示棱锥顶点到底边的高度，而不是边心距。不过公式是一样的。
因为三棱锥有三边，就需要让侧面积乘以1/2 * 3 。
底边长 b 对应了原公式里的 p 。 h 还是一致的。
3/2 * a * b 是最后剩下的底面三角形面积。
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4
应用在五棱锥上。 五棱锥的表面积公式： SA = (5/2 * b * h) + (5/2 * a * b)
SA、 b、 a 、h 都是一样的量。
(5/2 * b * h) 计算棱锥侧面积， (5/2 * a * b) 表示底面积。
五棱锥有五个侧面三角形。因此 1/2 要乘以 5 ，得到 (5/2 * b * h) 。
5/2 * b * a 就是最终整理的底面五边形面积。
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5
应用在六棱锥上。 六棱锥的表面积公式：SA = (3 * b * h) + (3 * a * b)
SA、 b、 a、 h 都是一样的量。
(3 * b * h) 是用来算侧面积的， (3 * a * b) 表示底面积。
因为有六个侧面，所以要把原公式的1/2 乘以 6 得到 3 * b * h 。
3 * b * a 是六边形的面积。
方法 2 的 5:
四棱锥表面积
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1
我们观察一下四棱锥的面积公式： SA = [2 * b * h] + b2
比如求底边围 3 cm ，斜高是 4 cm的四棱锥表面积。
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2
底边长和斜高乘起来。 得到侧面积一半。
例如： b * h = 3 * 4 = 12 cm2
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3
刚才的量乘以2 。 乘以2，可以得到侧面积。这是公式的第一半边。
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4
求出边长平方。 让底边得平方，得到底面面积，即公式的另一半。
比如： b2 = 32 = 3 * 3 = 9 cm2
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5
两者加起来。 这样可以得到总表面积。
比如： SA = [2 * b * h] + b2 = 24 * 9 = 216 cm2
方法 3 的 5:
三棱锥表面积
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1
查看其表面积公式：SA = (1/2 * a * b) + (3/2 * b * h)
比如要找出三棱锥表面积，其边心距是5 cm ，底边为 3 cm ，斜高为 6 cm。
a = 5 cm
b = 2 cm
h = 6 cm
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2
把边心距乘以底边长。 得到底面积两倍。
例如： a * b = 5 * 2 = 10 cm2
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3
除以2 。 这样可以得到底面积。即公式第一半边。
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4
将底边乘以斜高。 这样得到侧面积的一部分。
比如： b * h = 2 * 6 = 12 cm2
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5
将该积乘以3/2。 这样可以得到侧面积，算出公式另一部分。
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6
把两部分加起来。 得到表面积。
比如：SA = (1/2 * a * b) + (3/2 * b * h) = 5 + 18 = 23 cm2
方法 4 的 5:
五棱锥表面积
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1
看看如何应用公式：SA = (5/2 * b * h) + (5/2 * a * b)
比如我们要找五棱锥的表面积，其底边长为5 cm， 斜高为4 cm ，边心距是 6 cm。
b = 5 cm
h = 4 cm
a = 6 cm
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2
底边乘以斜高。 这样得到一部分侧面积。
如： b * h = 5 * 4 = 20 cm2
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3
这个积乘以 5/2，这样得到侧面积。 完成公式第一部分。
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4
把边心距乘以底边。 这样得到五边形一部分面积。
如： a * b = 6 * 5 = 30 cm2
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5
这个值乘以 5/2，得到底面积，完成公式另一部分。
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6
把两部分加起来，得到表面积。
例如： SA = (5/2 * b * h) + (5/2 * a * b) = 50 + 75 = 125 cm2
方法
5
方法 5 的 5:
六棱锥表面积
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1
查看表面积公式： SA = (3 * b * h) + (3 * a * b)
比如我们有个六棱锥，要找出表面积。其底边 3 cm，斜高 5 cm ，边心距 1 cm。
b = 3 cm
h = 5 cm
a = 1 cm
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2
把底边长乘以斜高。 得到一部分侧面积。
例如： b * h = 3 * 5 = 15 cm2
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3
这个值乘以3。 得到侧面积。这个值是公式一部分。
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4
把边心距乘以底边长，得到三分之一的底面积。
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5
然后再乘以3 。 这样得到底面积。完成公式第二部分。
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6
把两部分加起来。 这个步骤是最终步骤，得到表面积。
例如：SA = (3 * b * h) + (3 * a * b) = 45 + 9 = 54 cm2
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