Question

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

In this trapezoid:

• The parallel sides are the bases: \(b_1 = 6\) and \(b_2 = 8\).
• The perpendicular distance between these parallel bases is the height: \(h = 4\).

Step 2: Apply the trapezoid area formula

The area \(A\) of a trapezoid can be found by taking the average of the two parallel bases and multiplying by the height:

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

Substitute the given values into the formula:

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

Step 3: Calculate the final value

First, add the lengths of the bases:

$$6 + 8 = 14$$

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