Step 1: Find the area of the SEMICIRCLE (radius $14$ cm).\n Area$_\\text{semi}$ = $\\dfrac{1}{2} \\times \\pi \\times r^2 = \\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 14^2$\n = $\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 196$\n = $\\dfrac{22}{7} \\times 98$\n = $22 \\times 14 = 308$ cm².\n Step 2: Find the area of the QUARTER CIRCLE (radius $7$ cm).\n Area$_\\text{quarter}$ = $\\dfrac{1}{4} \\times \\pi \\times r^2 = \\dfrac{1}{4} \\times \\dfrac{22}{7} \\times 7^2$\n = $\\dfrac{1}{4} \\times \\dfrac{22}{7} \\times 49$\n = $\\dfrac{22}{7} \\times \\dfrac{49}{4}$\n = $\\dfrac{22 \\times 7}{4} = \\dfrac{154}{4} = 38.5$ cm².\n Step 3: Subtract because the quarter is CUT OUT.\n Remaining area = $308 - 38.5 = 269.5$ cm².\nCheck: $269.5 + 38.5 = 308$ (the original semicircle area) ✓. Answer: 269.5 cm²