Question

a hall is 24 metre long and 16 metre broad the area of its four wall is 640 m² find its height.​

Answer 1

Hello I am not sure about the answer but i have such formula like this.

Square(2- dimension) = Cube(3-dimention)

Rectangle (2-dimension) = Rectangular Prism(3- dimension)

In the given question, L = 15, B = 12

So, Area = l*b = 15*12 = 180 m²

Now, here we had calculated the area for Floor of the Hall & we know that area of both Floor and Ceiling in a hall will be equal, which means

Area of Floor = Area of Ceiling = 180m²

Hence, Sum of their area = 180+180 = 360m²

In the question, also they had mentioned that Sum of the area of Floor and Ceiling is equal to the sum of the area of four walls in a Hall.

Note:

Square = 4 sides are equal

Rectangle = only 2 opposite sides are equal

In case of 3-dimension,

If the hall is in Cube shape, the area of all the 4 walls will be equal. But, here we know that the hall is in Rectangular Prism shape, so only area of 2 opposite walls will be equal.

Area of two walls = 15*b + 15*b = 30b

Area of other two walls = 12*b + 12*b = 24b

Hence,

Their Sum = 30b + 24b = 54b

360 = 54b which means b = 360/54 = 20/3

Here, the breadth of the walls is equal to the height of the rectangular prism (Hall)

Hence,

Volume of Hall = l*b*h = 15*12*(20/3) = 1200 m³