https://file.aiquickdraw.com/mathbot/file/1730007158349huzi7bwn.jpg

To find the area of trapezoid \( PQRS \), given that \( PQ \parallel SR \), 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 parallel sides,
- \( h \) is the height (the perpendicular distance between the parallel sides).

### Step-by-Step Solution:

1. **Identify the Parallel Sides**:
   - \( PQ = 3 \) and \( SR = 8 \).

2. **Identify the Height**:
   - The distance between \( PQ \) and \( SR \) (height \( h \)) is the length of line segment \( PS \) or \( QR \), which is given as \( 4 \).

3. **Calculate the Area**:
   \[
   \text{Area} = \frac{1}{2} \times (3 + 8) \times 4
   \]
   \[
   = \frac{1}{2} \times 11 \times 4
   \]
   \[
   = \frac{1}{2} \times 44
   \]
   \[
   = 22
   \]

### Final Answer:
The area of \( PQRS \) is \( 22 \) square units.

Would you like further details or have any questions?

### Related Questions:
1. How do you calculate the area of other quadrilaterals like parallelograms or rectangles?
2. What are the conditions required for a quadrilateral to be classified as a trapezoid?
3. Can the trapezoid area formula be derived from basic geometry principles?
4. What is the significance of parallel sides in determining the height in trapezoids?
5. How does the formula change if both parallel sides are of equal length?

### Tip:
When working with shapes like trapezoids, always ensure you identify parallel sides correctly, as this will guide you in calculating the height and using the area formula accurately.

Learn how to find the area of the trapezoid PQRS, where PQ and SR are parallel sides. This problem uses the trapezoid area formula: (1/2) × (b1 + b2) × h. Includes step-by-step calculations with side lengths of 3 and 8 units, and height of 4 units. Suitable for middle school students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation