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The table below lists the lengths of the bases and the heights for three different trapezoids. Fill in the area for each trapezoid.

[tex]\[
\text{Area} = \frac{1}{2} (\text{base}_1 + \text{base}_2) \times \text{height}
\][/tex]

\begin{tabular}{|l|l|l|l|l|}
\hline
\text{Trapezoid} & \text{Base 1} & \text{Base 2} & \text{Height} & \text{Area} \\
\hline
\text{A} & 6 & 3 & 4 & \\
\hline
\text{B} & 15 & 7 & 9 & \\
\hline
\text{C} & 30 & 13 & 10 & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To determine the area for each trapezoid, follow these steps:

1. Understand the formula for the area of a trapezoid:
[tex]\[ \text{Area} = \frac{1}{2} \times (\text{base1} + \text{base2}) \times \text{height} \][/tex]

2. Calculate the area for Trapezoid A:
- Base 1 (base1_A) = 6
- Base 2 (base2_A) = 3
- Height (height_A) = 4
[tex]\[ \text{Area}_A = \frac{1}{2} \times (6 + 3) \times 4 = \frac{1}{2} \times 9 \times 4 = \frac{1}{2} \times 36 = 18.0 \][/tex]
So, the area of Trapezoid A is 18.0.

3. Calculate the area for Trapezoid B:
- Base 1 (base1_B) = 15
- Base 2 (base2_B) = 7
- Height (height_B) = 9
[tex]\[ \text{Area}_B = \frac{1}{2} \times (15 + 7) \times 9 = \frac{1}{2} \times 22 \times 9 = \frac{1}{2} \times 198 = 99.0 \][/tex]
So, the area of Trapezoid B is 99.0.

4. Calculate the area for Trapezoid C:
- Base 1 (base1_C) = 30
- Base 2 (base2_C) = 13
- Height (height_C) = 10
[tex]\[ \text{Area}_C = \frac{1}{2} \times (30 + 13) \times 10 = \frac{1}{2} \times 43 \times 10 = \frac{1}{2} \times 430 = 215.0 \][/tex]
So, the area of Trapezoid C is 215.0.

Using these results, the table with the areas filled in is as follows:

[tex]\[ \begin{tabular}{|l|l|l|l|l|} \cline{2-5} \text{} & \text{base 1} & \text{base 2} & \text{height} & \text{area} \\ \hline \text{Trapezoid A} & 6 & 3 & 4 & 18.0 \\ \cline{2-5} \text{Trapezoid B} & 15 & 7 & 9 & 99.0 \\ \cline{2-5} \text{Trapezoid C} & 30 & 13 & 10 & 215.0 \\ \cline{2-5} \end{tabular} \][/tex]

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