哪个图形包含的面积更大：边长为 2 厘米的正方形 边长为 3 厘米和 2 厘米的矩形 边长为 4 厘米、高 2 厘米的三角形？

正方形是一个有四个边和四个角的封闭二维图形。所有四个边的长度相等且彼此平行。

正方形是四边形，其中：

• 对边是平行的。
• 四边相等。
• 所有角度均为 90°。

正方形的面积

正方形的面积是包围在其边界内的空间。它由其两侧中任何一条的乘积给出，并以平方单位表示。通过公式，我们有，

正方形的面积 = 边 × 边

让我们假设正方形的边等于 S。

所以，

Area =  S². 

三角形的面积

三角形是包含在三个边内的二维图形，其长度可能相等，也可能不相等。该区域被认为是包含在三个边内的空间。三角形的高度将顶点连接到第三边底部的中点。现在。

让我们假设 h 是三角形的高度，b 是三角形的底，

所以，

面积 = 1/2 × 底 × 高

= 1/2 × b × h

矩形的面积

矩形的面积是包围在其边界内的空间。它由任何长度和宽度的乘积给出，并以平方单位表示。通过公式，我们有，

矩形的面积 = 长 x 宽

让我们假设矩形的长度等于 l，b 是宽度。

所以，

Area =  length × breadth. 

哪个图形包含的面积更大：边长为 2 厘米的正方形 边长为 3 厘米和 2 厘米的矩形 边长为 4 厘米、高 2 厘米的三角形？

解决方案：

According to the formulae computed above, we have, 

Area of a square = (side)^2. 

Here 

Side = 2 cm 

Therefore, Area = 2² cm²

= 4 cm² …..I

Area of rectangle = length x breadth

We have, 

length = 3 cm 

breadth = 2 cm 

Therefore, Area = 3 × 2 cm²

= 6 cm² …..II

And, area of triangle = 1/2 × Base × Height

= 1/2 × 4 × 2 cm²

= 4 cm²…. III

Therefore, on comparing, we have, 

Area of rectangle > Area of square = Area of triangle

类似问题

问题1：计算哪个形状包围的面积更大；

边长为 10 m 的正方形，

长 11 m 宽 10 m 的矩形，

高 20 m 底边 11 m 的三角形

解决方案：

As we know that

I. Area of square = Side × Side

Area of square = Side²

Given : Side of square is 10 m

Area of square = 10²

Area of square = 10 × 10

Area of square = 100 m²

II. Area of rectangle = Length × Breadth

Given : Length is 11 m and Breadth is 10 m

Area of rectangle = 11 × 10

Area of rectangle = 110 m²

III. Area of triangle = 1/2 × Base × Height

Given : Base is 11 m and Height is 20 m

 Area of triangle = 1/2 × 11 × 20

 Area of triangle = 110 m²

Therefore From I, II and III we get;

Area of square = 100 m²

Area of rectangle = 110 m²

Area of triangle = 110 m²

Thus,

Area of Rectangle = Area of triangle > Area of square.

问题2：计算这些形状中哪个形状会包围更多的面积？

半径为 20 厘米的圆（使用 π = 3.14）

底边为 40 厘米，高为 30 厘米的平行四边形

平行边长 15 厘米和 20 厘米，高 40 厘米的梯形

解决方案：

I. Area of circle = πr²

Given : Radius is 20 cm

Area of circle = 3.14 × 20 × 20 (Using π = 3.14)

Area of circle = 1256 cm²

II. Area of parallelogram = Base × Height 

Given : Base is 40 cm and Height is 30 cm

Area of parallelogram = 40 × 30

Area of parallelogram = 1200 cm²

III. Area of trapezium = 1/2 × (Sum of parallel sides) × Height

Given : Height is 40 cm and Parallel side are 15 cm and 20 cm

Area of trapezium = 1/2 × (15 + 20) × 40

Area of trapezium = 700 cm²

Therefore,

Area of circle (1256 cm²) > Area of parallelogram (1200 cm²) > Area of trapezium (700 cm²).

问题 3. 找出哪个图形的周长最大？

边长 50 m

长 65 m 宽 30 m 的矩形

边长为 65 m 的等边三角形

解决方案：

Here,

I. Perimeter of square = 4 × Side

Given : Side is 50 m

Perimeter of square = 4 × 50

Perimeter of square = 200 m

II. Perimeter of rectangle = 2 × (Length + Breadth)

Given : Length is 65 m and breadth is 30 m

Perimeter of rectangle = 2 × (65 + 30) 

Perimeter of rectangle = 2 × 95

Perimeter of rectangle = 190 m

III. Perimeter of Equilateral triangle = Side + Side + Side

Given : Side is 65 m

Perimeter of Equilateral triangle = 65 + 65 + 65

Perimeter of Equilateral triangle = 195 m

Therefore,

Perimeter of square = 200 m > Perimeter of Equilateral triangle = 195 m > Perimeter of rectangle = 190 m.

问题 4. 找出有多少个边长为 2 m 的小正方形和由一个边长为 8 m 的大正方形组成？

解决方案：

As we know that,

Area of square = Side × Side

Area of large square = 8 × 8 

Area of large square = 64 m²

Now,

Area of small square = Side × Side

Area of small square = 2 × 2

Area of small square = 4 m²

Further finding how many small squares can be formed from the large square

⇒ Area of large square/Area of small square

⇒ 64/4

⇒ 16 times

Therefore,

16 small square can be formed from a large square.