Question

Find the area of the top rectangle:
14 in
9 in
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
A, equals, 14, dot, 9
A=
14⋅9
A, equals, 126
A=
126
Find the area of the side rectangle:
Find the area of the side rectangle:
9 in
7 in
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
A, equals, 9, dot, 7
A=
9⋅7
A, equals, 63
A=
63
Find the area of the bottom rectangle:
Find the area of the bottom rectangle:
14 in
7 in
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
A, equals, 14, dot, 7
A=
14⋅7
A, equals, 98
A=
98
Notice that the full diagram has two of each of those rectangles:
126 in²
126 in²
63 in²
63 in²
98 in²
98 in²
Total Surface Area, equals, 2, left parenthesis, 126, right parenthesis, plus, 2, left parenthesis, 63, right parenthesis, plus, 2, left parenthesis, 98, right parenthesis
Total Surface Area=
2(126)+2(63)+2(98)
Total Surface Area, equals, 252, plus, 126, plus, 196
Total Surface Area=
252+126+196
Total Surface Area, equals, 574
Total Surface Area=
574
Bella used 574 square inches of wrapping paper.
use that example Shandra is decorating the outside of a box in the shape of a right rectangular prism. The figure below shows a net for the box.On the tactile printout of the following graphs, a is 99 inches, b is 1313 inches, and c is 1212 inches.
12 in
12 in
9 in
9 in
13 in
9 in
9 in
An image is shown. To download tactile, press SHIFT-CONTROL-U for UEB or SHIFT-CONTROL-E for Nemeth.
What is the surface area of the box, in square inches, that Shandra decorates?
Answer
Attempt 1 out of 2

A, equalsA=
in, squared in
2

Answer 1

To find the surface area of the box that Shandra is decorating, we first need to identify the dimensions of the box and calculate the area of each rectangular face in the net.

According to the values provided:

- \( a = 12 \) inches (width)
- \( b = 13 \) inches (length)
- \( c = 9 \) inches (height)

The formula for the surface area \( S \) of a rectangular prism (box) is:

\[
S = 2lw + 2lh + 2wh
\]

Where:
- \( l \) is the length
- \( w \) is the width
- \( h \) is the height

Substituting in the values:

1. Length \( l = 13 \) inches
2. Width \( w = 12 \) inches
3. Height \( h = 9 \) inches

Now substituting into the surface area formula:

\[
S = 2(13)(12) + 2(13)(9) + 2(12)(9)
\]

Calculating each part:

1. \( 2(13)(12) = 2 \times 156 = 312 \)
2. \( 2(13)(9) = 2 \times 117 = 234 \)
3. \( 2(12)(9) = 2 \times 108 = 216 \)

Now adding these areas together:

\[
S = 312 + 234 + 216
\]

Calculating the total:

1. \( 312 + 234 = 546 \)
2. \( 546 + 216 = 762 \)

Therefore, the total surface area of the box that Shandra decorates is:

\[
\text{Surface Area} = 762 \text{ square inches}
\]

So, the answer is:

**762 in²**.