The composite shape in the image consists of two distinct parts:

1. A trapezoid with the following dimensions:

   • Bottom base: 20 inches
   • Top base: 8 inches
   • Height: 8 inches
   • The slant height of each side of the trapezoid is 10 inches.

2. A semicircle placed on top of the trapezoid:

   • The diameter of the semicircle is 8 inches (since it matches the top base of the trapezoid).
   • Therefore, the radius of the semicircle is $\frac{8}{2} = 4$ inches.

Step 1: Perimeter Calculation

The perimeter consists of:

• The perimeter of the trapezoid (two slanted sides and the bottom base).
• The perimeter of the semicircle (its curved part).

1.1 Trapezoid's perimeter:

• Bottom base = 20 inches
• The two slanted sides = 10 inches each

The straight top edge is covered by the diameter of the semicircle, so we exclude it from the perimeter. The perimeter contribution from the trapezoid is: $P_{\text{trapezoid}} = 20 + 10 + 10 = 40 \, \text{inches}$

1.2 Semicircle's perimeter:

The curved part of the semicircle’s perimeter is half of the circumference of a full circle: $C_{\text{semicircle}} = \frac{1}{2} \times 2 \pi r = \pi r = 3.14 \times 4 = 12.56 \, \text{inches}$

Thus, the total perimeter of the shape is: $P_{\text{total}} = P_{\text{trapezoid}} + C_{\text{semicircle}} = 40 + 12.56 = 52.56 \, \text{inches}$

Step 2: Area Calculation

The total area consists of the area of the trapezoid and the area of the semicircle.

2.1 Trapezoid's area:

The area of a trapezoid is given by the formula: $A_{\text{trapezoid}} = \frac{1}{2} \times (b_1 + b_2) \times h$ Where:

• $b_1 = 20$ inches (bottom base)
• $b_2 = 8$ inches (top base)
• $h = 8$ inches (height)

Substituting these values: $A_{\text{trapezoid}} = \frac{1}{2} \times (20 + 8) \times 8 = \frac{1}{2} \times 28 \times 8 = 112 \, \text{square inches}$

2.2 Semicircle's area:

The area of a semicircle is half the area of a full circle: $A_{\text{semicircle}} = \frac{1}{2} \times \pi r^2 = \frac{1}{2} \times 3.14 \times 4^2 = \frac{1}{2} \times 3.14 \times 16 = 25.12 \, \text{square inches}$

2.3 Total area:

The total area is the sum of the areas of the trapezoid and the semicircle: $A_{\text{total}} = A_{\text{trapezoid}} + A_{\text{semicircle}} = 112 + 25.12 = 137.12 \, \text{square inches}$

Final Results:

• Perimeter: 52.56 inches
• Total area: 137.12 square inches

Would you like further details or have any questions? Here are 5 related questions to expand your understanding:

1. How would the perimeter change if the radius of the semicircle doubled?
2. What is the formula for the perimeter of a full circle and how would it be applied here?
3. How do you calculate the area of a trapezoid if the bases are not parallel?
4. If the trapezoid had different slant heights, how would that affect the perimeter calculation?
5. What if the shape were a full circle instead of a semicircle—how would the area change?

Tip: When working with composite shapes, always calculate areas and perimeters for individual parts before combining them for accurate results.