Question

Question
Use the image to answer the question.

An illustration shows a trapezoid with parallel sides on the top and bottom. The top side is 24 centimeters and bottom side is 20 centimeters. Two perpendicular dotted lines of 10 centimeters are drawn from the bottom vertices to the top side. The two perpendicular lines are denoted by 4 right angle symbols.

What is the area of the quadrilateral?

(1 point)
Responses

240 cm2
240 cm squared

220 cm2
220 cm squared

460 cm2
460 cm squared

480 cm2
480 cm squared

Answer 1

To calculate the area of the trapezoid, we can use the formula for the area of a trapezoid:

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

where \(b_1\) and \(b_2\) are the lengths of the two parallel sides, and \(h\) is the height (the distance between the two parallel sides).

From your description:
- The length of the top side (\(b_1\)) is 24 cm.
- The length of the bottom side (\(b_2\)) is 20 cm.
- The height (\(h\)) is 10 cm.

Now substitute the values into the formula:

\[
\text{Area} = \frac{1}{2} \times (24 + 20) \times 10
\]
\[
\text{Area} = \frac{1}{2} \times 44 \times 10
\]
\[
\text{Area} = \frac{440}{2}
\]
\[
\text{Area} = 220 \, \text{cm}^2
\]

Therefore, the area of the quadrilateral (the trapezoid) is **220 cm²**.