Find the area of a semicircle.
Understand the Problem
The question is asking for the calculation of the area of a semicircle. To solve this, we will use the formula for the area of a semicircle, which is (1/2) * π * r^2, where r is the radius of the semicircle.
Answer
The area of the semicircle is \( \frac{25}{2} \pi \) square units, approximately 39.25 square units.
Answer for screen readers
The area of the semicircle is ( \frac{25}{2} \pi ) square units, or approximately 39.25 square units.
Steps to Solve
- Identify the radius
First, determine the radius of the semicircle. If it's not given, you will need that to proceed. For example, let’s say the radius ( r = 5 ) units.
- Use the area formula
Substitute the radius into the area formula for a semicircle, which is given as:
$$ \text{Area} = \frac{1}{2} \pi r^2 $$
- Calculate the area
Plugging in the radius, the calculation will look like this: $$ \text{Area} = \frac{1}{2} \pi (5)^2 $$
- Simplify the expression
Execute the calculations: $$ = \frac{1}{2} \pi (25) $$ $$ = \frac{25}{2} \pi $$
- Final calculation
If you want a numerical approximation, use ( \pi \approx 3.14 ): $$ \text{Area} \approx \frac{25}{2} \times 3.14 = 39.25 \text{ square units} $$
The area of the semicircle is ( \frac{25}{2} \pi ) square units, or approximately 39.25 square units.
More Information
The area of a semicircle is half that of a full circle. The formula takes into account the unique shape of a semicircle and uses the radius to compute the area effectively.
Tips
- Forgetting to use half the area of a circle. Remember that the semicircle is only half, hence the ( \frac{1}{2} ) in the formula.
- Miscalculating the power of the radius. Double-check that ( r^2 ) is correctly applied.
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