A name tag is made of a rectangle measuring 14 cm by 7 cm with a semicircle of diameter 7 cm attached to one of the 7 cm sides. The straight edge of the semicircle lies exactly along that 7 cm side of the rectangle. Find the perimeter of the name tag. (Take π = 22/7.)
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Worked Solution
Step 1: Identify which edges form the boundary (perimeter) of the composite figure.
The boundary = the two long sides of the rectangle (each 14 cm) + the OTHER short side of the rectangle (7 cm) + the curved arc of the semicircle. The 7 cm side where the semicircle is attached is no longer on the outside.
Step 2: Find the arc length of the semicircle.
Full circumference of a circle with d = 7: C = π × d = 22/7 × 7 = 22 cm.
Semicircle arc = ½ × 22 = 11 cm.
Step 3: Add up all the boundary pieces.
Perimeter = 14 + 14 + 7 + 11 = 46 cm.
Final answer: 46 cm.
Answer: 46 cm
Correct answer: 46 cm
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