Question

The perimeter of the given figure with its top as a semi-circle is :

• A. 66
• B. 56
• C. 78
• D. 70

Hint:

To find the perimeter of this shape, walk along its outer edge and add up the lengths: 1. {Bottom straight edge:} 14. 2. {Left straight edge:} 10. 3. {Right straight edge:} 10. 4. {Curved top (semi-circle):}
Its diameter is the top straight edge of the rectangle, which is 14 (same as the bottom).
So, its radius is \(14/2 = 7\).
Length of a semi-circular arc = \(\pi \times \text{radius}\). Using \(\pi = 22/7\), this is \((22/7) \times 7 = 22\). 5. {Total Perimeter} = \(14 + 10 + 10 + 22 = 56\).

Answer 1

The Correct Option is B

Concept: The perimeter of a shape is the total length of its outer boundary. For this composite figure (a rectangle topped with a semi-circle), we need to sum the lengths of all the straight and curved parts that form the outside edge. Step 1: Identify the parts forming the outer boundary The given figure looks like a rectangle with a semi-circle placed on one of its longer sides. The outer boundary consists of:
The bottom straight side of the rectangle.
The two vertical straight sides of the rectangle.
The curved edge of the semi-circle on top. (Note: The straight side of the rectangle that forms the diameter of the semi-circle is {not} part of the outer perimeter of the composite figure, as it's an internal line.) Step 2: Determine the lengths of the straight sides from the diagram From the diagram:
Length of the bottom side of the rectangle = \(14\) units (let's assume meters or cm, as the unit isn't specified but will be consistent).
Length of each vertical side of the rectangle = \(10\) units. So, the contribution from these straight sides to the perimeter is \(14 + 10 + 10 = 34\) units. Step 3: Determine the length of the curved semi-circular part The top side of the rectangle, which serves as the diameter of the semi-circle, has a length of \(14\) units.
Diameter (\(d\)) of the semi-circle = \(14\) units.
Radius (\(r\)) of the semi-circle = Diameter / 2 = \(14 / 2 = 7\) units. (The "7" marked inside the semi-circle likely indicates this radius). The circumference (length of the curved part) of a full circle is given by the formula \(C = 2\pi r\). For a semi-circle, the length of its curved part is half of this: \(\frac{1}{2} \times 2\pi r = \pi r\). Using the common approximation \(\pi \approx \frac{22}{7}\): Length of the semi-circular arc = \(\pi r = \frac{22}{7} \times 7 = 22\) units. Step 4: Calculate the total perimeter of the figure The total perimeter is the sum of the lengths of all outer boundary parts: Perimeter = (Length of bottom side) + (Length of left vertical side) + (Length of right vertical side) + (Length of semi-circular arc) Perimeter = \(14 + 10 + 10 + 22\) units Perimeter = \(34 + 22\) units Perimeter = \(56\) units. Step 5: Match with the given options The calculated perimeter is 56 units. This corresponds to option (2).