The figure below is a net for a right rectangular prism. Its surface area is 102 m² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension. such as 2,8,18 and 9
To find the missing faces and dimension, first we need to understand how to calculate the surface area of a right rectangular prism. The surface area of a right rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Given that the total surface area is 102 m², we can fill in the areas of the faces that are already known:
lw = 16
lh = 18
wh = ?
Now we can plug these values into the surface area formula to find the missing dimension:
102 = 2(16) + 2(18) + 2wh
102 = 32 + 36 + 2wh
102 = 68 + 2wh
2wh = 34
wh = 17
So, the missing face has an area of 17 m². Since the area of the face is given by the product of its dimensions, we can now find the missing dimension:
17 = 2 * x
x = 8.5
Therefore, the missing dimension is 8.5.