Asked by random child who needs alot of help
Consider the three-dimensional below.
17cm left side
4 cm back 10cm bottom
Determine the total surface area of the figure. The formula chart is at the bottom of the page.
(4 points)
Area of the Left Side =
square centimeters
Area of the Back =
square centimeters
Area of the Bottom =
square centimeters
TOTAL surface area of the figure =
square centimeters
17cm left side
4 cm back 10cm bottom
Determine the total surface area of the figure. The formula chart is at the bottom of the page.
(4 points)
Area of the Left Side =
square centimeters
Area of the Back =
square centimeters
Area of the Bottom =
square centimeters
TOTAL surface area of the figure =
square centimeters
Answers
Answered by
GPT-4o mini
To determine the total surface area of the given three-dimensional figure, we need to first find the area of each specified side: the left side, the back, and the bottom.
1. **Area of the Left Side**:
The left side is typically a rectangle. Assuming the left side has a height of 17 cm and a width that corresponds to the bottom dimension (10 cm):
\[
\text{Area of the Left Side} = \text{Height} \times \text{Width} = 17 \, \text{cm} \times 10 \, \text{cm} = 170 \, \text{cm}^2
\]
2. **Area of the Back**:
The back side is also a rectangle. Assuming the back has a height of 17 cm and a depth that corresponds to the depth (or back dimension) of 4 cm:
\[
\text{Area of the Back} = \text{Height} \times \text{Depth} = 17 \, \text{cm} \times 4 \, \text{cm} = 68 \, \text{cm}^2
\]
3. **Area of the Bottom**:
The bottom is a rectangle as well, corresponding to the bottom dimensions of the figure (width of 10 cm and depth of 4 cm):
\[
\text{Area of the Bottom} = \text{Width} \times \text{Depth} = 10 \, \text{cm} \times 4 \, \text{cm} = 40 \, \text{cm}^2
\]
Now, we can sum the areas of these three sides to find the **total surface area** of the figure (since the figure appears to have only these three sides exposed):
\[
\text{TOTAL Surface Area} = \text{Area of the Left Side} + \text{Area of the Back} + \text{Area of the Bottom} = 170 \, \text{cm}^2 + 68 \, \text{cm}^2 + 40 \, \text{cm}^2
\]
\[
\text{TOTAL Surface Area} = 278 \, \text{cm}^2
\]
**Summary**:
- Area of the Left Side = \(170 \, \text{cm}^2\)
- Area of the Back = \(68 \, \text{cm}^2\)
- Area of the Bottom = \(40 \, \text{cm}^2\)
- TOTAL surface area of the figure = \(278 \, \text{cm}^2\)
1. **Area of the Left Side**:
The left side is typically a rectangle. Assuming the left side has a height of 17 cm and a width that corresponds to the bottom dimension (10 cm):
\[
\text{Area of the Left Side} = \text{Height} \times \text{Width} = 17 \, \text{cm} \times 10 \, \text{cm} = 170 \, \text{cm}^2
\]
2. **Area of the Back**:
The back side is also a rectangle. Assuming the back has a height of 17 cm and a depth that corresponds to the depth (or back dimension) of 4 cm:
\[
\text{Area of the Back} = \text{Height} \times \text{Depth} = 17 \, \text{cm} \times 4 \, \text{cm} = 68 \, \text{cm}^2
\]
3. **Area of the Bottom**:
The bottom is a rectangle as well, corresponding to the bottom dimensions of the figure (width of 10 cm and depth of 4 cm):
\[
\text{Area of the Bottom} = \text{Width} \times \text{Depth} = 10 \, \text{cm} \times 4 \, \text{cm} = 40 \, \text{cm}^2
\]
Now, we can sum the areas of these three sides to find the **total surface area** of the figure (since the figure appears to have only these three sides exposed):
\[
\text{TOTAL Surface Area} = \text{Area of the Left Side} + \text{Area of the Back} + \text{Area of the Bottom} = 170 \, \text{cm}^2 + 68 \, \text{cm}^2 + 40 \, \text{cm}^2
\]
\[
\text{TOTAL Surface Area} = 278 \, \text{cm}^2
\]
**Summary**:
- Area of the Left Side = \(170 \, \text{cm}^2\)
- Area of the Back = \(68 \, \text{cm}^2\)
- Area of the Bottom = \(40 \, \text{cm}^2\)
- TOTAL surface area of the figure = \(278 \, \text{cm}^2\)
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