Math Problem Statement

Work out the area of this semicircle. Take π to be 3.142 and give your answer to 2 decimal places.

Solution

To find the area of the semicircle, follow these steps:

  1. Find the radius (r):

    • The diameter of the semicircle is given as 11 cm.
    • Radius r=112=5.5r = \frac{11}{2} = 5.5 cm.
  2. Use the area formula for a semicircle: Area=12πr2\text{Area} = \frac{1}{2} \pi r^2

  3. Plug in the values: Area=12×3.142×(5.5)2\text{Area} = \frac{1}{2} \times 3.142 \times (5.5)^2

  4. Calculate: Area=12×3.142×30.25\text{Area} = \frac{1}{2} \times 3.142 \times 30.25 Area=12×95.8855\text{Area} = \frac{1}{2} \times 95.8855 Area=47.94275\text{Area} = 47.94275

  5. Round to two decimal places: Area47.94cm2\text{Area} \approx 47.94 \, \text{cm}^2

So, the area of the semicircle is approximately 47.94cm247.94 \, \text{cm}^2.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of a Circle
Decimals

Formulas

Area of a semicircle = (1/2) × π × r²

Theorems

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Suitable Grade Level

Grades 6-8