11.3 Areas of Combinations of Plane Figures

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Key Formulas

Solved Examples

Step 1

  1. Analyze the Figure: We have a square. Two semicircles are drawn inside it, with diameters AD and BC.

Step 2

  1. Identify Dimensions: Side of square a=14a = 14 cm. The semicircles are on the sides, so their diameter is 14 cm. Radius r=7r = 7 cm.

Step 3

  1. Formulate Strategy: The shaded region is the part of the square not covered by the semicircles. Area = Area(Square) - [Area(Semicircle 1) + Area(Semicircle 2)].

Step 4

  1. Combine Shapes: Two semicircles of same radius make one full circle. Area = Area(Square) - Area(Circle).

Step 5

  1. Calculate: Asquare=14×14=196 cm2A_{\text{square}} = 14 \times 14 = 196 \text{ cm}^2. Acircle=πr2=227×7×7=154 cm2A_{\text{circle}} = \pi r^2 = \frac{22}{7} \times 7 \times 7 = 154 \text{ cm}^2.

Step 6

  1. Final Result: Area = 196−154=42 cm2196 - 154 = 42 \text{ cm}^2.
Final Answer

42 cm²

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