An HDB courtyard pavement is made from a SQUARE of side $14$ cm with a SEMICIRCLE attached to one side. The diameter of the semicircle is equal to the side of the square (so the semicircle bulges outward from the square). Find the TOTAL area of the composite figure. (Use $\pi = \dfrac{22}{7}$.)
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Worked Solution
Step 1: Split the composite figure into a square + a semicircle. The two parts do NOT overlap, so the total area is the sum of their areas.\n
Step 2: Area of the square = side × side = $14 \times 14 = 196$ cm².\n
Step 3: The semicircle has DIAMETER equal to the side of the square (14 cm), so its radius is $r = 14 \div 2 = 7$ cm.\n
Step 4: Area of the semicircle = $\dfrac{1}{2} \times \pi \times r^2 = \dfrac{1}{2} \times \dfrac{22}{7} \times 7 \times 7 = \dfrac{1}{2} \times 154 = 77$ cm².\n
Step 5: Total area = $196 + 77 = 273$ cm².\nCheck: 273 − 196 = 77 cm²; 77 × 2 = 154; 154 ÷ (22/7) = 49 = 7². ✓
Answer: 273 cm²
Correct answer: 273 cm²
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