Question
What is the area of the sides?
3 in, 4 in, 7 in
A. 7+3=10x2=20in
B. 7x3x2=42in
C. 7x3=21in
3 in, 4 in, 7 in
A. 7+3=10x2=20in
B. 7x3x2=42in
C. 7x3=21in
Answers
GPT-4o mini
To determine the area of the sides of a shape like a rectangular prism (a box), you need to find the area of each pair of opposite sides. Assuming the dimensions you provided (3 in, 4 in, and 7 in) are the lengths of the edges of a rectangular prism, the side areas can be calculated as follows:
The rectangles formed by the dimensions are:
1. Two sides of dimensions 3 in and 4 in (area = 3 in × 4 in);
2. Two sides of dimensions 4 in and 7 in (area = 4 in × 7 in);
3. Two sides of dimensions 3 in and 7 in (area = 3 in × 7 in).
Now calculating each area:
1. Area of the first pair of sides:
\[
2 \times (3 \text{ in} \times 4 \text{ in}) = 2 \times 12 \text{ in}^2 = 24 \text{ in}^2
\]
2. Area of the second pair of sides:
\[
2 \times (4 \text{ in} \times 7 \text{ in}) = 2 \times 28 \text{ in}^2 = 56 \text{ in}^2
\]
3. Area of the third pair of sides:
\[
2 \times (3 \text{ in} \times 7 \text{ in}) = 2 \times 21 \text{ in}^2 = 42 \text{ in}^2
\]
Adding these together gives the total surface area of the sides:
\[
24 \text{ in}^2 + 56 \text{ in}^2 + 42 \text{ in}^2 = 122 \text{ in}^2
\]
None of your choices A, B, or C correctly match the total area calculation. However, option C (7 × 3 = 21 in²) corresponds to the area of one pair of opposing sides but does not represent the total area. The correct approach yields a total of 122 in² for all sides of the shape.
The rectangles formed by the dimensions are:
1. Two sides of dimensions 3 in and 4 in (area = 3 in × 4 in);
2. Two sides of dimensions 4 in and 7 in (area = 4 in × 7 in);
3. Two sides of dimensions 3 in and 7 in (area = 3 in × 7 in).
Now calculating each area:
1. Area of the first pair of sides:
\[
2 \times (3 \text{ in} \times 4 \text{ in}) = 2 \times 12 \text{ in}^2 = 24 \text{ in}^2
\]
2. Area of the second pair of sides:
\[
2 \times (4 \text{ in} \times 7 \text{ in}) = 2 \times 28 \text{ in}^2 = 56 \text{ in}^2
\]
3. Area of the third pair of sides:
\[
2 \times (3 \text{ in} \times 7 \text{ in}) = 2 \times 21 \text{ in}^2 = 42 \text{ in}^2
\]
Adding these together gives the total surface area of the sides:
\[
24 \text{ in}^2 + 56 \text{ in}^2 + 42 \text{ in}^2 = 122 \text{ in}^2
\]
None of your choices A, B, or C correctly match the total area calculation. However, option C (7 × 3 = 21 in²) corresponds to the area of one pair of opposing sides but does not represent the total area. The correct approach yields a total of 122 in² for all sides of the shape.