面积为16900平方米的正方形的对角线长度是多少？

面积为16900m ²的正方形的对角线长度是多少？

正方形是与四个相等且平行的边相关联的二维图形。所有边的长度相等。正方形的角对应的所有角都等于直角。

正方形可以被视为具有以下属性的四边形：

• 对边是平行的。
• 四边相等。
• 所有角度均为 90°。

广场面积

区域是包围在对象边界内的空间。正方形的面积可以用正方形任意一条边的长度来衡量。正方形的所有边都相等，因此其最终面积等于边的正方形。

Area of the square using sides;

Area of square = side × side = side²

正方形的对角线

正方形包含两条对角线，它们是通过连接正方形的相对两侧而形成的。正方形的对角线与以下一组属性相关联：

• 正方形的对角线长度相等。
• 它们是彼此的垂直平分线。
• 对角线将它分成两个全等等腰直角三角形。

使用对角线的正方形面积

让我们考虑一个边 s 的正方形。由于所有边都相等，因此，每一边都等价于 s。

现在，

在三角形 ABC 中，

AB = s

公元前=s

让我们假设对角线 AC 为 d。

现在，在毕达哥拉斯定理中，

对角线 AC ² = AB ² + BC ² （由毕达哥拉斯定理）

AC = √(AB ² + BC ² )

AC = √(s ² + s ² )

AC = √2s

现在，面积 = 1/2 × d ^2，其中 d 是正方形的对角线。

面积为16900 m ²的正方形的对角线长度是多少？

解决方案：

Area of square = side × side

Assume the side of the square be ‘s’

Area of square = s²

Here area of the square is given 16900 m²

Putting the value of the area in the formula

16900 = s²

s = √16900

s = 130 m

Thus,

Side of the square is 130 m

Now finding the diagonal of the square using its side

Diagonal AC² = AB² + BC²   (By Pythagoras theorem)

AC =  √(AB² + BC²)

AC = √(130² + 130²)

AC = 130√2 m

Therefore,

The length of the diagonal of the square of area 16900 m² is 130√2 m.

示例问题

问题1.如果正方形的对角线是60厘米，那么求正方形的面积？

解决方案：

Here we have to find the area of the square using the given diagonal,

We are given that the diagonal of the square is 60 cm

As we know that

Area of square = 1/2 d²

Here d is the diagonal

Area of the square = 1/2 × d²

Area of the square = 1/2 × 60 × 60

Area of the square = 1800 cm²

Therefore,

Area of the square with a diagonal of 60 cm is 1800 cm².

问题 2. 如果正方形的面积是 2500 m ² ，求它的对角线？

解决方案：

Here we have to find the diagonal of the square whose area is given

Given the area of the square is 2500 m²

As we know that

Area of the square = Side × Side

Assume the side of the square be ‘s’

Area of the square = s²

2500 = s²

s = √2500

s = 50 cm

Further,

As we know that

Diagonal of the square = side√2

Diagonal of the square = s√2

Diagonal of the square = 50√2 cm

Therefore,

The diagonal of the square with the area 2500 cm² is 50√2 cm.

问题 3. 求对角线为 100 厘米的正方形的周长？

解决方案：

Here we have to find the perimeter of the square whose diagonal is given

Here we have

Diagonal = 100 cm

As we know that

Diagonal of the square = side√2

Assume the side of the square be ‘s’

100 = s√2

s = 100/√2 cm

Now,

Perimeter of the square = 4 × side

Perimeter of the square = 4 × s

Perimeter of the square = 4 × 100/√2

Perimeter of the square = 400/√2 cm

Therefore,

Perimeter of the square is 400/√2.

问题 4. 如果一个广场公园的对角线是 75√2 m，那么以每米 50 卢比的比率计算围起广场公园的成本？

解决方案：

Here we have to find the cost of fencing the square park

As we know that

Diagonal of square = side√2

Assume the side of the square park is ‘s’

75√2 = s√2

s = 75 m

Thus, 

Side of the square park is 75 m

Now,

Finding the cost of fencing

Perimeter of square = 4 × side

Perimeter of square = 4 × 75

Perimeter of square = 300 m

Cost of fencing = ₹50 × 300

Cost of fencing = ₹15000

Therefore,

Cost of fencing square park is ₹15000.

问题 5. 求对角线为120 厘米的正方形的面积？

解决方案：

Here we have to find the area of the square using the given diagonal,

We are given that the diagonal of the square is 120 cm

As we know that

Area of square = 1/2 d²

Here d is the diagonal

Area of the square = 1/2 × d²

Area of the square = 1/2 × 120 × 120

Area of the square = 7200 cm²

Therefore,

Area of the square with a diagonal of 120 cm is 7200 cm².