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Question

Find the perimeter of the semi-circle of radius 21 cm.
$\left(\text{Take } \pi = \frac{22}{7}\right)$

The correct answer is
108 cm

To find the perimeter of a semi-circle, you need to consider both the curved part of the semi-circle and the diameter (straight line across).

  1. First, find the curved part of the semi-circle. The formula for the circumference of a full circle is: \(C = 2\pi r\) Given that the radius \(r = 21 \text{ cm}\) and \(\pi = \frac{22}{7}\), the circumference of the full circle would be: \(C = 2 \times \frac{22}{7} \times 21\).
  2. Simplify the calculation:
    • First, multiply: \(2 \times 21 = 42\)
    • Then multiply by \(\frac{22}{7}\)\(42 \times \frac{22}{7} = 132\)
  3. The length of the curved part of the semi-circle is half of the full circumference: \(\frac{132}{2} = 66 \text{ cm}\).
  4. The diameter of the circle also forms part of the semi-circle perimeter. This is twice the radius: \(D = 2 \times 21 = 42 \text{ cm}\).
  5. Add the curved part and the diameter to find the total perimeter of the semi-circle: \(66 + 42 = 108 \text{ cm}\).

Thus, the perimeter of the semi-circle is 108 cm, which is the correct answer.

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Important Questions from Mensuration 2D (Notes)

  1. Find the area of a quadrilateral ABCD whose area is twice the area of a triangle PQR. The sides of triangle PQR are in the ratio 4:5:6 and the perimeter of the triangle is 90 cm (use $\sqrt{7} = 2.6$).
  2. Find the area of a regular hexagon whose side measures $14\sqrt{3}$ cm.
  3. The length of a diagonal of a rectangular park is 25 meters, and that of one of its sides is 15 meters. Find the perimeter of the park.
  4. If the area of an equilateral triangle is given as $900 \text{ m}^2$, then what is its perimeter?
  5. The difference between two parallel sides of a trapezium is 9 cm. The perpendicular distance between them is 52 cm. If the area of the trapezium is 988 \(cm^2\), find the lengths of the parallel sides (in cm).

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