Question
The picture shows the front panel of a handbag. Substitute the values shown into the formula for the area of a trapezoid to create an equation that can be used to find the area of the front of the handbag. What is the equation?
With the width of 25 cm and the height is 15 cm and the height is 13 cm.
A = __cm^2
With the width of 25 cm and the height is 15 cm and the height is 13 cm.
A = __cm^2
Answers
GPT-4o mini
To find the area of a trapezoid, you can use the formula:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where:
- \( A \) is the area,
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases) of the trapezoid,
- \( h \) is the height (the distance between the two bases).
From your description, it seems that one base (width) is 25 cm and you have two heights given (15 cm and 13 cm). However, typically a trapezoid has two distinct bases and one height. Could you confirm which values belong to the bases and which one is the height?
Assuming:
- \( b_1 = 25 \) cm (the longer base),
- \( b_2 \) = (The second base has to be defined; let's assume it's 15 cm based on what you've given as the height),
- and \( h = 13 \) cm (the height of the trapezoid).
Then, the area can be calculated by substituting these values into the trapezoid area formula.
Assuming \( b_2 = 15 \) cm, we can substitute it into the formula:
\[
A = \frac{1}{2} \times (25 + 15) \times 13
\]
Now, calculate this:
1. Add the bases: \( 25 + 15 = 40 \)
2. Now use the formula:
\[
A = \frac{1}{2} \times 40 \times 13
\]
3. Calculate:
\[
A = 20 \times 13 = 260
\]
Therefore, the equation for the area of the trapezoid, assuming \( b_2 = 15 \) cm, is:
\[
A = \frac{1}{2} \times (25 + 15) \times 13
\]
And the computed area is:
\[
A = 260 \, \text{cm}^2
\]
Please clarify if there are any changes needed for \( b_2 \) or the height to provide a more accurate equation!
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where:
- \( A \) is the area,
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases) of the trapezoid,
- \( h \) is the height (the distance between the two bases).
From your description, it seems that one base (width) is 25 cm and you have two heights given (15 cm and 13 cm). However, typically a trapezoid has two distinct bases and one height. Could you confirm which values belong to the bases and which one is the height?
Assuming:
- \( b_1 = 25 \) cm (the longer base),
- \( b_2 \) = (The second base has to be defined; let's assume it's 15 cm based on what you've given as the height),
- and \( h = 13 \) cm (the height of the trapezoid).
Then, the area can be calculated by substituting these values into the trapezoid area formula.
Assuming \( b_2 = 15 \) cm, we can substitute it into the formula:
\[
A = \frac{1}{2} \times (25 + 15) \times 13
\]
Now, calculate this:
1. Add the bases: \( 25 + 15 = 40 \)
2. Now use the formula:
\[
A = \frac{1}{2} \times 40 \times 13
\]
3. Calculate:
\[
A = 20 \times 13 = 260
\]
Therefore, the equation for the area of the trapezoid, assuming \( b_2 = 15 \) cm, is:
\[
A = \frac{1}{2} \times (25 + 15) \times 13
\]
And the computed area is:
\[
A = 260 \, \text{cm}^2
\]
Please clarify if there are any changes needed for \( b_2 \) or the height to provide a more accurate equation!