In the following diagram, a circle is inscribed in a square. How can you find the area of the shaded region?
Notice that the shaded region of the figure is composed of four identical pieces. However, each piece has a curved side, which makes it very difficult to find its area using a direct method. In this type of diagram, the easiest way to find the area uses an indirect method. Look at the diagram using a different perspective. The shaded region is composed of four identical pieces. OR, the shaded region is the area of the square minus the area of the circle. Since you know how to find the area of both a square and a circle, this is a much easier method for solving!
Area of square: s2 = (6 cm)2 = 36 cm2
Area of circle: r2 ≈ (3.14)(3 cm)2 ≈(3.14)(9 cm2) ≈ 28.26 cm2
Area of shaded region: 36 cm2 - 28.26 cm2 = 7.74 cm2
The area of the shaded region is approximately 7.74 square centimeters.
Answer the questions based on the following diagram. Note: The two triangles meet at the center of the circle.
What is the approximate area of the circle? Use 3.14 in your calculation.
What is the area of one of the triangles?
What is the approximate area of the shaded region of the diagram?
