Area Of A Semicircle Combined With a Parallelogram

🔑 Key Concepts

  • A composite figure is made from two or more basic shapes.
  • The area of a parallelogram is \(A=bh\).
  • The base and perpendicular height are \(10\) units and \(7\) units.
  • Opposite sides of a parallelogram are congruent, so the semicircle’s diameter is \(8\) units.
  • The semicircle therefore has a radius of \(4\) units.
  • Find each area separately and add the results.

💡 Main Idea

Separate the composite figure into a parallelogram and a semicircle. The parallelogram has a base of \(10\) units and a perpendicular height of \(7\) units. Its slanted side measures \(8\) units, so the congruent opposite side forming the semicircle’s diameter also measures \(8\) units. Divide the diameter by \(2\) to find a radius of \(4\), calculate both areas, and add them.

✏️ Worked Example - Composite Area

🧠 Math Vocabulary

  • Composite figure: A figure made by combining two or more basic geometric shapes.
  • Parallelogram: A quadrilateral with two pairs of parallel opposite sides.
  • Base: The side of a figure used with its corresponding perpendicular height to calculate area.
  • Perpendicular height: The shortest distance from a base to the opposite parallel side.
  • Opposite sides: Sides of a polygon that do not share a vertex. Opposite sides of a parallelogram are congruent.
  • Semicircle: Half of a circle.
  • Diameter: A segment passing through a circle’s center with endpoints on the circle.
  • Radius: A segment from a circle’s center to a point on the circle; it is half the diameter.
  • Area: The amount of two-dimensional space inside a figure, measured in square units.

📚 What You Should Already Know

You should know how to identify the base and perpendicular height of a parallelogram and use \(A=bh\). You should also know that opposite sides of a parallelogram are congruent. For the semicircle, remember that the radius is half the diameter and that its area is half the area of a complete circle.

🚀 What Comes Next

Next, you can find the areas of composite figures involving rectangles, triangles, trapezoids, parallelograms, circles, and semicircles. Some problems may require finding an unmarked dimension, subtracting a missing region, or interpreting figures drawn on coordinate grids.

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