Question
The figure is composed of two trapezoids. The length of each side is given in centimeters.
the top part: 8 cm
The sides: 5 cm
the middle length: 6 cm
the bottom part: 9 cm
What is the area of the figure in square centimeters?
the top part: 8 cm
The sides: 5 cm
the middle length: 6 cm
the bottom part: 9 cm
What is the area of the figure in square centimeters?
Answers
GPT-4o mini
To find the area of the figure composed of two trapezoids, we can break it down into two individual trapezoids and calculate their areas separately.
1. **Top trapezoid:**
- Top base (length) = 8 cm
- Bottom base (length) = 6 cm
- Height (length of the sides) = 5 cm (since both sides are equal)
The formula for the area \( A \) of a trapezoid is:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.
Plugging in the values for the top trapezoid:
\[
A_{top} = \frac{1}{2} \times (8 \, \text{cm} + 6 \, \text{cm}) \times 5 \, \text{cm
} = \frac{1}{2} \times 14 \, \text{cm} \times 5 \, \text{cm} = \frac{70}{2} = 35 \, \text{cm}^2
\]
2. **Bottom trapezoid:**
- Top base (length) = 6 cm (this is the bottom of the top trapezoid which is the top base of the bottom trapezoid)
- Bottom base (length) = 9 cm
- Height = 5 cm
Using the trapezoid area formula again:
\[
A_{bottom} = \frac{1}{2} \times (6 \, \text{cm} + 9 \, \text{cm}) \times 5 \, \text{cm}
\]
Simplifying:
\[
A_{bottom} = \frac{1}{2} \times 15 \, \text{cm} \times 5 \, \text{cm} = \frac{75}{2} = 37.5 \, \text{cm}^2
\]
3. **Total area of the figure:**
Now, we combine the areas of both trapezoids:
\[
A_{total} = A_{top} + A_{bottom} = 35 \, \text{cm}^2 + 37.5 \, \text{cm}^2 = 72.5 \, \text{cm}^2
\]
Thus, the area of the figure is \( \boxed{72.5} \) square centimeters.
1. **Top trapezoid:**
- Top base (length) = 8 cm
- Bottom base (length) = 6 cm
- Height (length of the sides) = 5 cm (since both sides are equal)
The formula for the area \( A \) of a trapezoid is:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.
Plugging in the values for the top trapezoid:
\[
A_{top} = \frac{1}{2} \times (8 \, \text{cm} + 6 \, \text{cm}) \times 5 \, \text{cm
} = \frac{1}{2} \times 14 \, \text{cm} \times 5 \, \text{cm} = \frac{70}{2} = 35 \, \text{cm}^2
\]
2. **Bottom trapezoid:**
- Top base (length) = 6 cm (this is the bottom of the top trapezoid which is the top base of the bottom trapezoid)
- Bottom base (length) = 9 cm
- Height = 5 cm
Using the trapezoid area formula again:
\[
A_{bottom} = \frac{1}{2} \times (6 \, \text{cm} + 9 \, \text{cm}) \times 5 \, \text{cm}
\]
Simplifying:
\[
A_{bottom} = \frac{1}{2} \times 15 \, \text{cm} \times 5 \, \text{cm} = \frac{75}{2} = 37.5 \, \text{cm}^2
\]
3. **Total area of the figure:**
Now, we combine the areas of both trapezoids:
\[
A_{total} = A_{top} + A_{bottom} = 35 \, \text{cm}^2 + 37.5 \, \text{cm}^2 = 72.5 \, \text{cm}^2
\]
Thus, the area of the figure is \( \boxed{72.5} \) square centimeters.