How to Find the Area of a Semicircle

Step-by-step solution

1. Find the area of the full circle.

   $$A = \pi r^2 = \pi \times 6^2 = 36\pi$$

   Why: Start with the whole circle, then cut it in half.

2. Halve the area.

   $$\frac{36\pi}{2} = 18\pi$$

   Why: A semicircle is exactly half of a circle.

3. Estimate with pi about 3.14.

   $$18 \times 3.14 \approx 56.5$$

   Why: The exact answer stays in terms of pi; the decimal is a check.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $r = 4$

   Show answer

   $A = 8\pi$

2. 2

   $r = 10$

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   $A = 50\pi$

3. 3

   $r = 2$

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   $A = 2\pi$

4. 4

   $r = 8$

   Show answer

   $A = 32\pi$

5. 5

   $r = 5$

   Show answer

   $A = \frac{25\pi}{2}$