A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π

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Question: A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 22/7)

Options:

Correct Answer: 77 cm²

Solution:

Radius = 7 cm. Area of semicircle = (1/2) × πr² = (1/2) × (22/7) × (7)² = 77 cm².

A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 22/7)

A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 22/7)

Step 1: Identify the diameter of the semicircle, which is given as 14 cm.
Step 2: Calculate the radius of the semicircle by dividing the diameter by 2. So, radius = 14 cm / 2 = 7 cm.
Step 3: Use the formula for the area of a semicircle, which is (1/2) × π × r².
Step 4: Substitute the value of π with 22/7 and the radius (r) with 7 cm into the formula: Area = (1/2) × (22/7) × (7)².
Step 5: Calculate (7)², which is 49.
Step 6: Now substitute 49 into the formula: Area = (1/2) × (22/7) × 49.
Step 7: Multiply (22/7) by 49. This gives you 22 × 7 = 154.
Step 8: Now, divide 154 by 2 to find the area: Area = 154 / 2 = 77 cm².

Area of a Semicircle – The area of a semicircle is calculated using the formula A = (1/2) × πr², where r is the radius.
Understanding Diameter and Radius – The radius is half of the diameter, which is crucial for calculating the area.
Approximation of π – Using an approximate value for π (22/7) is necessary for the calculation.