1. **Shape a**: Two quarter circles joined at a right angle, height 28 cm. - Each quarter circle radius $r=28$ cm. - Perimeter = sum of two quarter circle arcs + two straight edges. - Arc length of one quarter circle = $\frac{1}{4} \times 2\pi r = \frac{\pi r}{2}$. - Total arc length = $2 \times \frac{\pi r}{2} = \pi r = \pi \times 28 = 87.9646$ cm. - Straight edges = $28 + 28 = 56$ cm. - Perimeter = $87.965 + 56 = 143.965$ cm, rounded to 3 sig figs: $144$ cm. - Area = sum of two quarter circle areas = half circle area = $\frac{1}{2} \pi r^2 = 0.5 \times \pi \times 28^2 = 1231.504$ cm$^2$, rounded: $1230$ cm$^2$. 2. **Shape b**: Three circles arranged in a triangle, height 1.3 cm, base 1.5 cm. - Assuming equilateral triangle with side $s=1.5$ cm. - Area of equilateral triangle = $\frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \times 1.5^2 = 0.974$ cm$^2$. - Perimeter of triangle = $3 \times 1.5 = 4.5$ cm. - Circles' radii not given, so perimeter and area refer to triangle. 3. **Shape c**: Two radii forming 100° angle, length 3.2 cm. - Sector area = $\frac{100}{360} \pi r^2 = \frac{5}{18} \pi \times 3.2^2 = 8.91$ cm$^2$. - Arc length = $\frac{100}{360} \times 2\pi r = \frac{5}{18} \times 2\pi \times 3.2 = 5.59$ cm. - Perimeter = sum of two radii + arc length = $3.2 + 3.2 + 5.59 = 11.99$ cm, rounded: $12.0$ cm. 4. **Shape d**: Upper semicircle width 11 cm, lower semicircle width 7 cm, smaller section 3 cm. - Radii: $r_1=\frac{11}{2}=5.5$ cm, $r_2=\frac{7}{2}=3.5$ cm. - Perimeter = semicircle arcs + straight edges. - Upper semicircle arc = $\pi r_1 = \pi \times 5.5 = 17.28$ cm. - Lower semicircle arc = $\pi r_2 = \pi \times 3.5 = 10.995$ cm. - Straight edges = 3 cm (given). - Total perimeter = $17.28 + 10.995 + 3 = 31.275$ cm, rounded: $31.3$ cm. - Area = sum of two semicircle areas + rectangle area. - Semicircle areas: $\frac{1}{2} \pi r_1^2 = 47.52$ cm$^2$, $\frac{1}{2} \pi r_2^2 = 19.24$ cm$^2$. - Rectangle area = $3 \times 7 = 21$ cm$^2$. - Total area = $47.52 + 19.24 + 21 = 87.76$ cm$^2$, rounded: $87.8$ cm$^2$. 5. **Shape e**: Square 10 cm by 8 cm joined to quarter circle radius 4 cm. - Perimeter = square perimeter minus one side + quarter circle arc + radius side. - Square perimeter = $2(10+8) = 36$ cm. - Remove one side (8 cm) where quarter circle joins. - Quarter circle arc = $\frac{1}{4} \times 2\pi r = \frac{\pi r}{2} = \frac{\pi \times 4}{2} = 6.283$ cm. - Add radius side (4 cm) to perimeter. - Total perimeter = $36 - 8 + 6.283 + 4 = 38.283$ cm, rounded: $38.3$ cm. - Area = square area + quarter circle area = $10 \times 8 + \frac{1}{4} \pi 4^2 = 80 + 12.566 = 92.566$ cm$^2$, rounded: $92.6$ cm$^2$. **Final answers:** - a) Perimeter = $144$ cm, Area = $1230$ cm$^2$ - b) Perimeter = $4.5$ cm, Area = $0.974$ cm$^2$ - c) Perimeter = $12.0$ cm, Area = $8.91$ cm$^2$ - d) Perimeter = $31.3$ cm, Area = $87.8$ cm$^2$ - e) Perimeter = $38.3$ cm, Area = $92.6$ cm$^2$