Calculate Trapezoid Side Length: Given Area 120 and Height 10

To solve this problem, we will follow these steps:

• Step 1: Identify the given information from the problem statement.
• Step 2: Use the formula for the area of a trapezoid.
• Step 3: Plug in the values and solve for the unknown base $DC$.

Let's apply these steps:

Step 1: You're given:

• The height $h = 10$.
• The base $AB = 11$.
• The area of the trapezoid $= 120$.

Step 2: The formula for the area of a trapezoid is:

$\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h$

We know $b_1 = AB = 11$, $b_2 = DC$, $h = 10$, and $\text{Area} = 120$.

Step 3: Substitute the known values into the formula and solve for $DC$:

$120 = \frac{1}{2} \times (11 + DC) \times 10$

Simplify the equation:

$120 = 5 \times (11 + DC)$

Divide both sides by 5 to solve for $11 + DC$:

$24 = 11 + DC$

Subtract 11 from both sides:

$DC = 24 - 11$

Therefore, $DC = 13$.

Thus, the length of side $DC$ is $13$.