1. Problem 4(a): Find the perimeter and area of a semicircle with diameter 28 cm. - Radius $r = \frac{28}{2} = 14$ cm. - Perimeter of semicircle = half circumference + diameter = $\pi r + 2r = 14\pi + 28$ cm. - Area of semicircle = half area of circle = $\frac{1}{2} \pi r^2 = \frac{1}{2} \pi (14)^2 = 98\pi$ cm$^2$. 2. Problem 4(b): Shape with semicircle diameter 10 cm and rectangle length 14 cm. - Radius $r = 5$ cm. - Semicircle perimeter = $\pi r + 2r = 5\pi + 10$ cm. - Rectangle perimeter contribution (only 3 sides since one side is semicircle diameter): $14 + 10 + 14 = 38$ cm. - Total perimeter = semicircle arc + 2 rectangle sides = $5\pi + 14 + 14 = 5\pi + 28$ cm. - Area = semicircle area + rectangle area = $\frac{1}{2} \pi (5)^2 + 14 \times 10 = \frac{25\pi}{2} + 140$ cm$^2$. 3. Problem 4(c): Semicircle diameter 21 cm attached to rectangle length 36 cm. - Radius $r = 10.5$ cm. - Perimeter = semicircle arc + 2 rectangle sides = $\pi r + 2 \times 36 = 10.5\pi + 72$ cm. - Area = semicircle area + rectangle area = $\frac{1}{2} \pi (10.5)^2 + 21 \times 36 = \frac{110.25\pi}{2} + 756 = 55.125\pi + 756$ cm$^2$. 4. Problem 4(d): Circle diameter 7 cm with two chords 5.7 cm each. - Radius $r = 3.5$ cm. - Perimeter = circumference = $2\pi r = 7\pi$ cm. - Area = $\pi r^2 = \pi (3.5)^2 = 12.25\pi$ cm$^2$. - Chords do not affect perimeter or area. 5. Problem 4(e): Rectangle length 9 cm with semicircular indentations on all sides. - Vertical indentations radius = 2 cm, horizontal indentations radius = 3 cm. - Perimeter = rectangle perimeter minus straight sides replaced by semicircles plus semicircle arcs. - Total perimeter = $2(9 + 2 \times 2) - 4 \times 2 + 4 \times \pi \times r$ for semicircles. - Simplify: rectangle perimeter = $2(9 + 4) = 26$ cm. - Subtract straight sides replaced by semicircles: $4 \times 2 = 8$ cm. - Add semicircle arcs: $4 \times \pi \times r$ where $r$ alternates 2 and 3 cm semicircles. - Total semicircle arc length = $2 \times \pi \times 2 + 2 \times \pi \times 3 = 4\pi + 6\pi = 10\pi$ cm. - Final perimeter = $26 - 8 + 10\pi = 18 + 10\pi$ cm. - Area = rectangle area minus semicircle indentations area. - Rectangle area = $9 \times (2+2) = 9 \times 4 = 36$ cm$^2$. - Area of 4 semicircles = $2 \times \frac{1}{2} \pi 2^2 + 2 \times \frac{1}{2} \pi 3^2 = 2\pi + 9\pi = 11\pi$ cm$^2$. - Area left = $36 - 11\pi$ cm$^2$. 6. Problem 4(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 = $5\pi + 28$ cm, Area = $\frac{25\pi}{2} + 140$ cm$^2$. (c) Perimeter = $10.5\pi + 72$ cm, Area = $55.125\pi + 756$ cm$^2$. (d) Perimeter = $7\pi$ cm, Area = $12.25\pi$ cm$^2$. (e) Perimeter = $18 + 10\pi$ cm, Area = $36 - 11\pi$ cm$^2$. (f) Perimeter = $126\pi$ cm, Area = $2009\pi$ cm$^2$.