Area of a Semicircle and a Trapezoid Combined

🔑 Key Concepts

  • A composite figure is made from two or more basic shapes.
  • The trapezoid has bases of \(10\) units and \(4\) units and a height of \(6\) units.
  • The \(4\)-unit top base is also the diameter of the semicircle.
  • The semicircle therefore has a radius of \(2\) units.
  • Find each area separately and then add the results.

💡 Main Idea

This composite figure can be separated into an isosceles trapezoid and a semicircle. Use \(A=\frac{1}{2}(b_1+b_2)h\) to find the area of the trapezoid. The top base of the trapezoid is also the semicircle’s diameter, so divide \(4\) by \(2\) to obtain a radius of \(2\). Find half the area of the corresponding circle and add it to the trapezoid’s area.

✏️ Worked Example - Calculating Area of Composite Figures

🧠 Math Vocabulary

  • Composite figure: A figure made by combining two or more basic geometric shapes.
  • Trapezoid: A quadrilateral with at least one pair of parallel sides.
  • Base of a trapezoid: Either of the trapezoid’s parallel sides.
  • Perpendicular height: The shortest distance between the two parallel bases.
  • Semicircle: Half of a circle.
  • Diameter: A segment through a circle’s center with endpoints on the circle.
  • Radius: A segment from the center of a circle to a point on the circle.
  • 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 two parallel bases and perpendicular height of a trapezoid. You should also know how to use the area formulas for a trapezoid and a circle. Remember that the radius is half the diameter and that the area of a semicircle is half the area of a complete circle.

🚀 What Comes Next

Next, you can find the areas of more complex composite figures involving rectangles, triangles, parallelograms, circles, semicircles, and shaded regions. You may also need to subtract missing sections or use dimensions found indirectly from other measurements.

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