Question
Find the surface area of figure.
Diagram shows a rectangle on the bottom and trapizoid on top.
Dimensions on rectangle is width 12 m, height 6m,.
Trapezoid is across top is 8m down the slant is 20m .shows height at the back of both rectangle and trapezoid 22m.
Diagram shows a rectangle on the bottom and trapizoid on top.
Dimensions on rectangle is width 12 m, height 6m,.
Trapezoid is across top is 8m down the slant is 20m .shows height at the back of both rectangle and trapezoid 22m.
Answers
GPT-4o mini
To find the surface area of the figure composed of a rectangle at the bottom and a trapezoid on top, we will calculate the area of each shape separately and then sum them.
### Step 1: Calculate the area of the rectangle
The rectangle has the following dimensions:
- Width: \( 12 \, \text{m} \)
- Height: \( 6 \, \text{m} \)
The area \( A_{\text{rectangle}} \) of the rectangle is given by:
\[
A_{\text{rectangle}} = \text{Width} \times \text{Height} = 12 \, \text{m} \times 6 \, \text{m} = 72 \, \text{m}^2
\]
### Step 2: Calculate the area of the trapezoid
The trapezoid has:
- Base 1 (top base) = \( 8 \, \text{m} \)
- Base 2 (bottom base, equal to width of rectangle) = \( 12 \, \text{m} \)
- Height = \( 22 \, \text{m} - 6 \, \text{m} = 16 \, \text{m} \) (the total height of the trapezoid is the total height minus the height of the rectangle)
The area \( A_{\text{trapezoid}} \) of the trapezoid is given by the formula:
\[
A_{\text{trapezoid}} = \frac{1}{2} (b_1 + b_2) \times h
\]
Where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.
Plugging in the values:
\[
A_{\text{trapezoid}} = \frac{1}{2} (8 \, \text{m} + 12 \, \text{m}) \times 16 \, \text{m}
\]
\[
= \frac{1}{2} (20 \, \text{m}) \times 16 \, \text{m} = 10 \, \text{m} \times 16 \, \text{m} = 160 \, \text{m}^2
\]
### Step 3: Calculate the total surface area
Now, we can find the total surface area \( A_{\text{total}} \) by summing the areas of the rectangle and the trapezoid:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{trapezoid}} = 72 \, \text{m}^2 + 160 \, \text{m}^2 = 232 \, \text{m}^2
\]
Therefore, the total surface area of the figure is \(\boxed{232 \, \text{m}^2}\).
### Step 1: Calculate the area of the rectangle
The rectangle has the following dimensions:
- Width: \( 12 \, \text{m} \)
- Height: \( 6 \, \text{m} \)
The area \( A_{\text{rectangle}} \) of the rectangle is given by:
\[
A_{\text{rectangle}} = \text{Width} \times \text{Height} = 12 \, \text{m} \times 6 \, \text{m} = 72 \, \text{m}^2
\]
### Step 2: Calculate the area of the trapezoid
The trapezoid has:
- Base 1 (top base) = \( 8 \, \text{m} \)
- Base 2 (bottom base, equal to width of rectangle) = \( 12 \, \text{m} \)
- Height = \( 22 \, \text{m} - 6 \, \text{m} = 16 \, \text{m} \) (the total height of the trapezoid is the total height minus the height of the rectangle)
The area \( A_{\text{trapezoid}} \) of the trapezoid is given by the formula:
\[
A_{\text{trapezoid}} = \frac{1}{2} (b_1 + b_2) \times h
\]
Where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.
Plugging in the values:
\[
A_{\text{trapezoid}} = \frac{1}{2} (8 \, \text{m} + 12 \, \text{m}) \times 16 \, \text{m}
\]
\[
= \frac{1}{2} (20 \, \text{m}) \times 16 \, \text{m} = 10 \, \text{m} \times 16 \, \text{m} = 160 \, \text{m}^2
\]
### Step 3: Calculate the total surface area
Now, we can find the total surface area \( A_{\text{total}} \) by summing the areas of the rectangle and the trapezoid:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{trapezoid}} = 72 \, \text{m}^2 + 160 \, \text{m}^2 = 232 \, \text{m}^2
\]
Therefore, the total surface area of the figure is \(\boxed{232 \, \text{m}^2}\).