1. Problem: Find the perimeter and area of each figure where circular portions are semicircles, all dimensions in cm. (a) Semicircle with diameter 28 cm and a horizontal line below. - Radius $r=\frac{28}{2}=14$ cm. - Perimeter = semicircle arc + diameter = $\pi r + 28 = 14\pi + 28$ cm. - Area = half circle area = $\frac{1}{2}\pi r^2 = \frac{1}{2}\pi (14)^2 = 98\pi$ cm$^2$. (b) Quarter circle with radius 14 cm and inner segment 10 cm. - Perimeter = quarter circle arc + two radii = $\frac{1}{4} (2\pi r) + 2r = \frac{1}{2}\pi (14) + 28 = 7\pi + 28$ cm. - Area = quarter circle area = $\frac{1}{4}\pi r^2 = \frac{1}{4}\pi (14)^2 = 49\pi$ cm$^2$. (c) Semicircle with diameter 36 cm and height 21 cm inside. - Radius $r=\frac{36}{2}=18$ cm. - Perimeter = semicircle arc + diameter = $\pi r + 36 = 18\pi + 36$ cm. - Area = half circle area = $\frac{1}{2}\pi r^2 = \frac{1}{2}\pi (18)^2 = 162\pi$ cm$^2$. (d) Sector with radius 7 cm, sides 5.7 cm, base 8 cm. - Perimeter = sum of sides + arc length. - Arc length = perimeter - sides = $8 + 5.7 + 5.7 = 19.4$ cm total perimeter, arc length = $19.4 - (5.7+5.7) = 8$ cm. - Area of sector = $\frac{1}{2} r \times \text{arc length} = \frac{1}{2} \times 7 \times 8 = 28$ cm$^2$. (e) Rectangle 9 cm by 3 cm with quarter circle cutouts radius 2 cm at corners. - Rectangle perimeter = $2(9+3) = 24$ cm. - Each quarter circle arc length = $\frac{1}{4} 2\pi r = \frac{1}{4} 2\pi (2) = \pi$ cm. - Total arc length for 4 corners = $4 \times \pi = 4\pi$ cm. - Adjusted perimeter = rectangle perimeter - straight edges replaced + arcs = $24 - 8 + 4\pi = 16 + 4\pi$ cm. - Area rectangle = $9 \times 3 = 27$ cm$^2$. - Area cutouts = 4 quarter circles = 1 full circle area = $\pi (2)^2 = 4\pi$ cm$^2$. - Area remaining = $27 - 4\pi$ cm$^2$. (f) Two overlapping circles with diameters 56 cm and 70 cm. - Perimeter = sum of circumferences = $\pi \times 56 + \pi \times 70 = 56\pi + 70\pi = 126\pi$ cm. - Area = sum of areas = $\pi (28)^2 + \pi (35)^2 = 784\pi + 1225\pi = 2009\pi$ cm$^2$. Final answers: (a) Perimeter = $14\pi + 28$ cm, Area = $98\pi$ cm$^2$. (b) Perimeter = $7\pi + 28$ cm, Area = $49\pi$ cm$^2$. (c) Perimeter = $18\pi + 36$ cm, Area = $162\pi$ cm$^2$. (d) Perimeter = $19.4$ cm, Area = $28$ cm$^2$. (e) Perimeter = $16 + 4\pi$ cm, Area = $27 - 4\pi$ cm$^2$. (f) Perimeter = $126\pi$ cm, Area = $2009\pi$ cm$^2$.