哪个图形包围的面积更大：边长为 2 厘米的正方形还是长 3 厘米宽 2 厘米的长方形？
面积定义为二维形状占据的空间量。以不同的方式，我们可以说它是计算覆盖任何封闭/有界图形表面的单位正方形数量的数量。面积的标准单位是平方单位，一般用平方米、平方英尺、平方英寸、平方厘米等来表示。
闭合形状的面积是根据其长度和宽度计算的。长度是单向的，其单位是米（m）、厘米（cm）、码（yd）、英寸（in）等。但是，形状的面积是一个二维量，即长宽的乘积。因此，它以平方厘米或 (cm 2 )、平方米 (m 2 ) 平方英尺或 (ft 2 ) 等平方单位进行测量。
如何测量任何图形的面积？
我们将在网格的帮助下理解这个概念，每个网格由许多 1 个 1 个单位的边正方形组成。每个正方形的面积是 1 个正方形单位。因此我们可以说每个方格是 1 个方格单位。看下图。让我们找出在网格中绘制的形状的面积。
彩色区域的面积是阴影单位正方形的数量
形状的面积 = 7 个平方单位。因为每个盒子是一个方格，总共有7个彩色方格，所以它的方格是7个方格。
不同几何形状的面积
如果 l 是长度，b 是宽度，h 是几何形状的高度。
广场面积
Area of square = side × side = side2 square units.
For example: if side of square is 6 m then its area will be 6 × 6 m2 = 36 m2
矩形面积
Area of rectangle = length × breadth square units
for example: if the length and breadth of rectangle are 6 and 8 cm then its area will be 6 × 8 cm2 = 48 cm2
圆的面积
Area of circle = π r2 square units
r is the radius of circle
for example: if radius of circle is 7 cm then its area is π 7 × 7 = 22/7 × 7 × 7 = 154 cm2
三角形面积
Area of triangle = 1/2 × base × height = b × h square units
for example: if base and height of triangle are 4 and 6 cm respectively, then area of triangle is 1/2 × 4 × 6 = 12 cm2
平行四边形的面积
Area of a parallelogram = base × height = b × h square units
for example if base and height of triangle are 5 and 6 cm respectively, then area of parallelogram is 5 × 6 = 30 cm2.
菱形面积
Area of Rhombus = 1/2 × (d1) × (d2) square units
哪个图形包围的面积更大：边长为 2 厘米的正方形还是长 3 厘米宽 2 厘米的长方形？
解决方案：
First consider, square
Length of square = 2 cm
Area of square = side2
A = 22
A = 4 cm2
Now, consider rectangle
length of rectangle = 3 cm
breadth of rectangle = 2 cm
Area of rectangle = length × breadth = 3 × 2 cm2
A’ = 6 cm2
Now after comparing values of A and A’ we see that the area of A’ is greater which means that area of rectangle is greater than square.
示例问题
问题1：正方形的边是7厘米，计算它的面积。
解决方案：
Side of square = 7 cm
Area of a square = side × side.
A = 7 × 7 = 49
Therefore, the area of the square = 49 cm2.
问题 2：如果一个长方形的面积是 120 平方厘米，其中一个尺寸是 15 厘米，计算另一个。
解决方案：
Given,
let length of rectangle, l = 15 cm
Area of rectangle, A = 120 cm2.
Area of rectangle = length × breadth
120 = 15 × b
=> b = 120/15
b = 8 cm.
Hence, other dimension of rectangle is 8cm.
问题3：如果宽5厘米的长方形面积等于边长10厘米的正方形的面积，长方形的长度是多少？
解决方案：
Area of square = side x side
A = 10 × 10 square cm.
A = 100 square cm
Now,
Area of rectangle = length × breadth
A’ = l × 5
A’ = 5l square cm
According to question :
Area of square = Area of rectangle
=> A’ = A
5l = 100
l = 100/5 = 20 cm
Length of rectangle is 20cm
问题 4：如果菱形的对角线是 20 厘米和 48 厘米，求菱形的周长。
解决方案：
Given diagonal d1 = 48 cm
diagonal d2 = 20 cm
Rhombus with diagonals 48 and 20 cm
OA = AD/2 = 20/2 = 10cm
OC = BC/2 = 48/2 = 24cm
In triangle AOC
Using pythagoras theorem
AC2 = OA2+ OC2
AC = √(10)2 + (24)2
AC = √100+ 576 = √676 = 26cm
Perimeter of rhombus = 4 × side
= 4 × 26 = 104cm
问题5：如果正方形的边变成两倍，正方形的面积会怎样。
解决方案：
Let, the side of square be s
now the Area of square = side × side
A = s2 square cm
If the side s doubles then, New side
s’ = 2s
Area of new square = side × side= s’ × s’
A’ = 2s × 2s = 4s2
A’ = 4 × A —— (A = s2)
=> Area of square will increases four times if we double its side.
问题 6：如果正方形的边变成一半，正方形的面积会发生什么变化。
解决方案：
Let, the side of square be s
Now the Area of square = side × side
A = s2 square cm
If the side s half then, New side
s’ = s/2
Area of new square = side × side = s’ × s’
A’ = s/2 × s/2 = s2/4
A’ = A/4 —— (A = s2)
=> Area of square will decrease to one-forth times if we half its side.