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The figure below is a net for a right rectangular prism. Its surface area is 340 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, b is 40 centimeters squared, c is 50 centimeters squared, e is 8 centimeters, and f is 5 centimeters. The missing face is labeled A and the missing dimension is labeled with a question mark.

40 cm²
40 cm²
50 cm²
50 cm²
5 cm
5 cm
8 cm
8 cm
8 cm
8 cm
?
?
A
A
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Find the area of the missing faces:
Find the area of the missing faces:
Total Surface Area, equals, 2, left parenthesis, 40, right parenthesis, plus, 2, left parenthesis, 50, right parenthesis, plus, 2, left parenthesis, A, right parenthesis
Total Surface Area=
2(40)+2(50)+2(A)
340, equals, 2, left parenthesis, 40, right parenthesis, plus, 2, left parenthesis, 50, right parenthesis, plus, 2, left parenthesis, A, right parenthesis
340=
2(40)+2(50)+2(A)
340, equals, 80, plus, 100, plus, 2, left parenthesis, A, right parenthesis
340=
80+100+2(A)
340, equals, 180, plus, 2, left parenthesis, A, right parenthesis
340=
180+2(A)
minus, 180, minus, 180
−180=
−180
160, equals, 2, A
160=
2A
start fraction, 160, divided by, 2, end fraction, equals, start fraction, 2, A, divided by, 2, end fraction
2
160
​
=
2
2A
​

80, equals, A
80=
A
The area of the missing face is 80 cm².
The area of the missing face is 80 cm².
Label diagram with found areas:
Label diagram with found areas:
8
?
?
8
?
?
5
?
?
8
?
?
8
5
5
5
5
8
8
40
40
50
50
80
80
An image is shown. To download tactile, press SHIFT-CONTROL-U for UEB or SHIFT-CONTROL-E for Nemeth.
Use one of the faces to find the missing edge:
Use one of the faces to find the missing edge:
?
8
80
An image is shown. To download tactile, press SHIFT-CONTROL-U for UEB or SHIFT-CONTROL-E for Nemeth.
A, equals, l, w
A=
lw
80, equals, left parenthesis, 8, right parenthesis, left parenthesis, question mark, right parenthesis
80=
(8)(?)
start fraction, 80, divided by, 8, end fraction, equals, start fraction, left parenthesis, 8, right parenthesis, left parenthesis, question mark, right parenthesis, divided by, 8, end fraction
8
80
​
=
8
(8)(?)
​

10, equals, question mark
10=
?
The area of each missing face is 80 cm².
The area of each missing face is 80 cm².
The length of each missing edge is 10 cm.
The length of each missing edge is 10 cm.
use this exanmple to answer this
The figure below is a net for a right rectangular prism. Its surface area is 152 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, b is 48 centimeters squared, c is 16 centimeters squared, e is 6 centimeters, and f is 8 centimeters. The missing face is labeled A and the missing dimension is labeled with a question mark.
48 cm²
48 cm²
16 cm²
16 cm²
8 cm
8 cm
6 cm
6 cm
6 cm
6 cm
?
?
A
A
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Answer
Attempt 1 out of 2

The area of each missing face is
centimeters squared cm²
The length of each missing edge is
centimeters cm
Submit Answer

1 answer

To find the area of the missing face (labeled A) and the missing dimension, we can follow similar steps to those illustrated in your provided example.

  1. Find Area of the Missing Faces:

    We know the total surface area of the prism is 152 cm². The areas of the given faces are:

    • Face b: 48 cm²
    • Face c: 16 cm²
    • There are two faces of each dimension 6 cm by 8 cm, which correspond to the other dimensions.

    The total surface area equation can be expressed as: \[ \text{Total Surface Area} = 2(\text{Area of Face b}) + 2(\text{Area of Face c}) + 2(\text{Area of Face A}) \]

    Plugging in the known values: \[ 152 = 2(48) + 2(16) + 2(A) \]

    Simplifying this: \[ 152 = 96 + 32 + 2A \] \[ 152 = 128 + 2A \]

    Now, subtract 128 from both sides: \[ 152 - 128 = 2A \] \[ 24 = 2A \] Dividing both sides by 2 gives us: \[ A = 12 \]

    So the area of the missing face is 12 cm².

  2. Find the Missing Dimension:

    Since face A corresponds to one of the dimensions of the prism, we can use the area of face A to find the missing edge.

    Given that we know the dimensions of face A must be the length (l) and width (w): \[ A = lw \] Plugging in the known values: \[ 12 = 6 \cdot ? \] To find the missing dimension, we can solve for "?": \[ ? = \frac{12}{6} = 2 \]

    So the length of each missing edge is 2 cm.

In summary:

  • The area of each missing face is 12 cm².
  • The length of the missing edge is 2 cm.