The worksheet asks for the following:

1. Finding the perimeter of the figure (a trapezoid).
2. Finding the area of the figure.

Step 1: Understanding the Given Dimensions

From the image:

• The top base of the trapezoid is 7 in.
• The bottom base of the trapezoid is 14 in.
• The height (perpendicular distance between the two bases) is 4 in.
• The slanted side (one of the non-parallel sides) is 8.06 in.

Solution:

1. Find the Perimeter

The perimeter is the sum of all the sides of the figure: $\text{Perimeter} = \text{Top base} + \text{Bottom base} + \text{Left side} + \text{Slanted side}.$

• Top base = 7 in.
• Bottom base = 14 in.
• Left side = 4 in.
• Slanted side = 8.06 in.

$\text{Perimeter} = 7 + 14 + 4 + 8.06 = 33.06 \, \text{in}.$

2. Find the Area

The area of a trapezoid is given by: $\text{Area} = \frac{1}{2} \cdot (\text{Top base} + \text{Bottom base}) \cdot \text{Height}.$

• Top base = 7 in.
• Bottom base = 14 in.
• Height = 4 in.

$\text{Area} = \frac{1}{2} \cdot (7 + 14) \cdot 4 = \frac{1}{2} \cdot 21 \cdot 4 = 42 \, \text{square inches}.$

Final Answers:

1. Perimeter: 33.06 in.
2. Area: 42 square inches.

Would you like more details or further explanation?

5 Related Questions:

1. What is the formula for the perimeter of other polygons like a triangle or rectangle?
2. Can you generalize the formula for the area of any quadrilateral?
3. How does changing the height affect the area of a trapezoid?
4. What are the differences between a trapezoid and a parallelogram?
5. What is the significance of the slanted side in determining the perimeter?

1 Tip:

Always label all dimensions clearly in geometry problems to avoid confusion when calculating area and perimeter.