Question

there is a pair of parallel sides in the following shape. what is the area of the shape? \\( \text{______ units}^2 \\)

Explanation:

🆕 New Concept Discovered: Area of a Trapezoid
Finding space inside a shape with one pair of parallel sides

Step 1: Identify the shape and its properties

The problem states that there is a pair of parallel sides in the shape. Looking at the diagram, the vertical sides of lengths \(6\) and \(8\) are parallel to each other. A quadrilateral with exactly one pair of parallel sides is a trapezoid.

The parallel sides are called the bases:

• Base 1 (\(b_1\)) = \(6\)
• Base 2 (\(b_2\)) = \(8\)

The perpendicular distance between these parallel bases is the height (\(h\)). The dashed line of length \(4\) is perpendicular to both vertical bases, which means:

• Height (\(h\)) = \(4\)

Step 2: Apply the trapezoid area formula

The area of a trapezoid is calculated by taking the average of the two parallel bases and multiplying by the height:

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

Substitute the values into the formula:

$$ \text{Area} = \frac{6 + 8}{2} \times 4 $$

Step 3: Calculate the final value

First, add the bases inside the parentheses:

$$ 6 + 8 = 14 $$

Next, divide by \(2\) to find the average base length:

$$ \frac{14}{2} = 7 $$

Finally, multiply by the height:

$$ 7 \times 4 = 28 $$

Answer:

28