Examples of composite shapes combining polygons and circular sectors for perimeter and area calculations.

- First, look closely: After zooming in on the green shape, I can see it's composed of a polygon and a quarter-circle. The polygon is an L-shape. The vertical part is 4 cm tall. The horizontal part at the bottom has a total length of 9 cm, with a central segment of 4 cm, meaning the two slanted sides are each (9 - 4) / 2 = 2.5 cm long. However, the diagram labels these slanted sides as 3.5 cm, which contradicts the total width of 9 cm if the central segment is 4 cm. This suggests the 3.5 cm is the length of the slanted side, not the horizontal projection. The height of the bottom part is 2 cm. The curved part is a quarter-circle with a radius of 4 cm, attached to the top left corner. For the perimeter, I need to add the outer edges: the arc of the quarter-circle, the vertical side (4 cm), the horizontal side (4 cm), the two slanted sides (3.5 cm each), and the bottom horizontal side (4 cm). For the area, I need to calculate the area of the polygon (which can be seen as a rectangle minus two triangles or as a trapezoid plus a rectangle) plus the area of the quarter-circle.

- Next, find information: I will now calculate the perimeter and area for the first shape (yellow).

Shape 1 (Yellow):

a) Perimeter:
- Bottom edge: 16 cm
- Left vertical edge: 7 cm
- Right vertical edge: 7 cm
- Top right horizontal edge: 6 cm
- Arc of semicircle: π * r = π * 5 cm ≈ 15.708 cm
Total Perimeter = 16 + 7 + 7 + 6 + 15.708 = 51.708 cm

b) Area:
- Area of large rectangle (16 cm x 7 cm): 112 cm²
- Area of small rectangle (6 cm x 7 cm): 42 cm²
- Area of semicircle (π * r² / 2): (π * 5²) / 2 = (25π) / 2 ≈ 39.27 cm²
Total Area = (112 - 42) + 39.27 = 70 + 39.27 = 109.27 cm²

Shape 2 (Green):

a) Perimeter:
- Arc of quarter-circle: (2πr) / 4 = (2π * 4) / 4 = 2π cm ≈ 6.283 cm
- Vertical edge: 4 cm
- Horizontal edge (top): 4 cm
- Two slanted edges: 3.5 cm + 3.5 cm = 7 cm
- Bottom horizontal edge: 4 cm
Total Perimeter = 6.283 + 4 + 4 + 7 + 4 = 25.283 cm

b) Area:
- Area of quarter-circle: (π * r²) / 4 = (π * 4²) / 4 = 4π cm² ≈ 12.566 cm²
- Area of polygon: Can be calculated as the area of a rectangle (9 cm x 2 cm) plus the area of the top part. The top part is a rectangle (4 cm x 2 cm) minus two right triangles. The base of each triangle is (9 - 4) / 2 = 2.5 cm, and the height is 2 cm. So, area of each triangle is (1/2) * 2.5 * 2 = 2.5 cm². Total area of polygon = (9 * 2) + (4 * 2) - (2 * 2.5) = 18 + 8 - 5 = 21 cm².
Total Area = 12.566 + 21 = 33.566 cm²

- Then, review the findings: I have calculated the perimeter and area for both shapes based on the given dimensions and my interpretation of the composite figures. The calculations for the yellow shape are straightforward. For the green shape, there was a slight ambiguity in the dimensions, but I resolved it by using the labeled lengths for the slanted sides and calculating the area accordingly.

- Final Answer:
- Shape 1 (Yellow):
a) Perimeter: 51.71 cm
b) Area: 109.27 cm²
- Shape 2 (Green):
a) Perimeter: 25.28 cm
b) Area: 33.57 cm²