he figure below is a net for a right rectangular prism. Its surface area is 310 cm² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension.On the tactile printout of the following graphs, d is 50 centimeters squared, c is 35 centimeters squared, g is 5 centimeters, and f is 7 centimeters. The missing face is labeled A and the missing dimension is labeled with a question mark.
To find the missing faces and dimension, we first need to identify the dimensions of the prism.
From the given information, we know the following about the filled-in faces:
- Face d = 50 cm² (bottom face)
- Face c = 35 cm² (top face)
- Face g = 5 cm (width of the prism)
- Face f = 7 cm (height of the prism)
We can find the area of the bottom and top faces (d and c) using the formula for the area of a rectangle: Area = length x width
Area of d = 50 cm²
50 = x(5)
x = 10 cm
Area of c = 35 cm²
35 = x(10)
x = 3.5 cm
So, the missing dimension (length of the prism) is 10 cm, and the missing faces are the two side faces (A). To find the area of the missing faces, we can use the surface area formula for a prism: Surface Area = 2lw + 2lh + 2wh
Given surface area = 310 cm²
Given length = 10 cm
Given height = 7 cm
Given width = 5 cm
Now we can calculate the area of the missing faces (A):
310 = 2(10)(7) + 2(10)(5) + 2(7)(5) + 2(A)
310 = 140 + 100 + 70 + 2A
2A = 310 - 140 - 100 - 70
2A = 0
A = 0
Therefore, the area of the missing faces is 0 cm², and the length of the prism is 10 cm.