如何求梯形的周长?
梯形是一种几何图形,包含一对相对的边,本质上是平行的。这些平行的边组称为底,梯形的非平行边称为腿。它可以被认为是具有两条平行边的平行四边形的特例。也称为梯形。
梯形的类型
梯形可分为以下三种类型:
- 等腰梯形
- 不等边梯形
- 右梯形
梯形的性质
梯形与以下属性相关联:
- 一对相对的边是平行的。
- 不相等的不平行边。例外是等腰梯形。
- 对角线相互交叉。
- 与非平行边的中点相交的线始终平行于底边。这些等于平行边总和的一半
梯形周长
由梯形或梯形的边形成的边界长度的总和称为梯形的周长。它是一个不规则的多边形。梯形的周长包含在二维形状中,因为所有的线和顶点都只包含在二维平面中。梯形的周长单位用以下单位表示,如“英寸”、“英尺”、“米”等。
Perimeter of trapezium = Sum of non-parallel sides + Sum of parallel sides
如何求梯形的周长?
回答:
The perimeter of the trapezoid can be found by performing the following steps:
Step 1: Compute the dimensions of all the sides of the trapezoid.
Step 2: Perform the summation of the lengths of all the sides.
Step 3: Compute its units.
梯形周长公式
让我们假设一个梯形 ABCD,其中 AB 和 CD 边彼此平行。它们形成一对“底”,而 AD 和 BC 是不平行的边(即它们是腿)。让我们假设梯形的周长等于“P”。单位。
The perimeter of trapezoid ABCD is given by,
P = AB + BC + CD + AD.
The perimeter of the trapezoid in terms of area is given by the following formula,
P = (sum of the lengths of non-parallel sides) + 2
where A is the area of trapezoid and h is its height.
示例问题
问题 1. 计算平行边为 4 厘米和 6 厘米的梯形的周长。非平行边 5 cm 和 8 cm?
解决方案:
Here we have,
The parallel sides are 4 cm and 6 cm
The non-parallel sides are 5 cm and 8 cm
To find the perimeter of the trapezium we need to add all the sides of the trapezium.
Perimeter of trapezium = Sum of parallel sides + sum of non-parallel sides
Perimeter of trapezium = 4 cm + 6 cm + 5 cm + 8 cm
Perimeter of trapezium = 23 cm
Therefore,
Perimeter of trapezium is 23 cm.
问题 2. 计算平行边 20 m 25 m 和非平行边 18 m 和 16 m 的梯形地面的周长?
解决方案:
Here we have to find the perimeter of the trapezium ground
We have,
The parallel sides are 20 m and 25 m
The non-parallel sides are 18 m and 16 m
To find the perimeter of the trapezium ground we need to add all the sides of the trapezium ground.
Perimeter of trapezium ground = Sum of parallel sides + sum of non-parallel sides
Perimeter of trapezium ground = 20 m + 25 m + 18 m + 16 m
Perimeter of trapezium ground = 79 m
Therefore,
Perimeter of trapezium ground is 79 cm.
问题 3. 如果梯形的周长是 54 厘米,平行边是 10 厘米和 15 厘米。假设不平行的边相等。然后找到两个不平行边的长度?
解决方案:
Here we have the perimeter of the trapezium 54 cm
We are given that the parallel sides are 10 cm and 15 cm
The non-parallel sides are equal
Assume that the non-parallel side is x.
Therefore,
The perimeter of the trapezium = 54 cm
The perimeter of the trapezium = 10 cm + 15 cm + x + x
54 = 25 + 2x
2x = 54 – 25
2x = 29
x =
x = 14.5 cm
Therefore the non-parallel side of the trapezium is 14.5 cm
As both the sides are equal
Hence,
Sides of the trapezium = 10 cm, 15 cm, 14.5 cm, 14.5 cm
问题 4. 计算平行边为 15 厘米×17 厘米的正梯形的周长,不平行边的长度为 8 厘米。
解决方案:
Here we are given,
Parallel side of the trapezium are 15 cm and 17 cm
Length of the non-parallel side is 8 cm, 8 cm
Therefore,
Perimeter of the trapezium = Sum of all the sides of the trapezium
Perimeter of the trapezium = 15 cm + 17 cm + 2(8)
= 15 cm + 17 cm + 16 cm
Perimeter of the trapezium = 48 cm
问题 5. 计算平行边为 25 厘米和 30 厘米的梯形的周长。非平行边 19 厘米和 18 厘米?
解决方案:
Here we have,
The parallel sides are 25 cm and 30 cm
The non-parallel sides are 19 cm and 18 cm
To find the perimeter of the trapezium we need to add all the sides of the trapezium.
Perimeter of trapezium = Sum of parallel sides + sum of non-parallel sides
Perimeter of trapezium = 25 cm + 30 cm + 19 cm + 18 cm
Perimeter of trapezium = 92 cm
Therefore,
Perimeter of trapezium is 92 cm.