The problem provided asks to find the perimeter ($P$) and area ($A$) of a trapezoid. Based on the image:

• The trapezoid has the following sides:
  • Two parallel sides: 2.5 m and 3 m
  • Two non-parallel sides: 2.3 m and the other side is missing (you will need it for the perimeter).

Perimeter Calculation

The perimeter ($P$) is the sum of all the sides of the trapezoid: $P = 2.5\,\text{m} + 3\,\text{m} + 2.3\,\text{m} + \text{missing side length}$ Without the length of the missing side, the exact perimeter cannot be determined, but based on your given calculation, it appears that you might have treated the missing side as 1.5 m. So: $P = 2.5\,\text{m} + 3\,\text{m} + 2.3\,\text{m} + 1.5\,\text{m} = 9.3\,\text{m}$ However, the perimeter was recorded as 7.8 m in your work, indicating a possible mistake or misunderstanding.

Area Calculation

The area ($A$) of a trapezoid is calculated using the formula: $A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$ Where:

• $\text{Base}_1 = 2.5\,\text{m}$
• $\text{Base}_2 = 3\,\text{m}$
• $\text{Height} = 2.3\,\text{m}$

Plugging in these values: $A = \frac{1}{2} \times (2.5\,\text{m} + 3\,\text{m}) \times 2.3\,\text{m} = \frac{1}{2} \times 5.5\,\text{m} \times 2.3\,\text{m} = 6.325\,\text{m}^2$

Thus, the area $A$ of the trapezoid is approximately 6.325 square meters.

Would you like more details or have any questions about this problem? Here are five related questions to expand on the topic:

1. What are the general properties of a trapezoid, and how do they differ from other quadrilaterals?
2. How can you determine the length of the missing side in a trapezoid if only the height and the other three sides are known?
3. What are some real-life applications of calculating the area and perimeter of trapezoids?
4. How does the area of a trapezoid change if the height is doubled while keeping the bases constant?
5. Can the formula for the area of a trapezoid be derived from the formula for the area of a triangle?

Tip: Always double-check your perimeter calculation to ensure all sides are accounted for correctly!