Understanding Regular Polygons and Composite Figures
In geometry, regular polygons are two-dimensional shapes with equal sides and equal angles. Composite figures, on the other hand, are shapes that can be divided into simpler shapes, such as triangles and rectangles. In this worksheet, we will explore the concepts of regular polygons and composite figures, and provide solutions to common problems.
Regular Polygons
Regular polygons have equal sides and equal angles. The number of sides of a polygon is called its degree. For example, a triangle has 3 sides, a quadrilateral has 4 sides, and a pentagon has 5 sides.
Properties of Regular Polygons:
- All sides are equal in length
- All angles are equal in measure
- The sum of the interior angles of a polygon is (n-2) × 180°, where n is the number of sides
Examples of Regular Polygons:
- Equilateral triangle (3 sides)
- Square (4 sides)
- Regular pentagon (5 sides)
- Regular hexagon (6 sides)
Composite Figures
Composite figures are shapes that can be divided into simpler shapes, such as triangles and rectangles. These figures can be used to solve problems involving perimeter, area, and volume.
Examples of Composite Figures:
- A triangle with a rectangle attached to one side
- A square with a triangle attached to one corner
- A circle with a triangle attached to one side
Solutions to Regular Polygons and Composite Figures Worksheet
Problem 1: Find the perimeter of a regular hexagon with side length 6 cm.
Solution: Since all sides of a regular polygon are equal, the perimeter is equal to 6 times the side length. Therefore, the perimeter is 6 × 6 = 36 cm.
Problem 2: Find the area of a composite figure consisting of a triangle with base 5 cm and height 6 cm, and a rectangle with length 8 cm and width 4 cm.
Solution: First, find the area of the triangle: (1⁄2) × base × height = (1⁄2) × 5 × 6 = 15 cm^2. Next, find the area of the rectangle: length × width = 8 × 4 = 32 cm^2. Finally, add the areas of the triangle and rectangle to find the total area: 15 + 32 = 47 cm^2.
Problem 3: Find the volume of a composite figure consisting of a rectangular prism with length 8 cm, width 4 cm, and height 6 cm, and a triangular prism with base 5 cm, height 6 cm, and depth 3 cm.
Solution: First, find the volume of the rectangular prism: length × width × height = 8 × 4 × 6 = 192 cm^3. Next, find the area of the triangular base: (1⁄2) × base × height = (1⁄2) × 5 × 6 = 15 cm^2. Then, multiply the area of the base by the depth to find the volume of the triangular prism: 15 × 3 = 45 cm^3. Finally, add the volumes of the rectangular and triangular prisms to find the total volume: 192 + 45 = 237 cm^3.
📝 Note: These solutions are just examples, and you may have different problems and solutions in your worksheet.
Summary
Regular polygons and composite figures are important concepts in geometry. Regular polygons have equal sides and equal angles, while composite figures can be divided into simpler shapes. By understanding the properties and formulas of these shapes, you can solve problems involving perimeter, area, and volume.
What is a regular polygon?
+A regular polygon is a two-dimensional shape with equal sides and equal angles.
What is a composite figure?
+A composite figure is a shape that can be divided into simpler shapes, such as triangles and rectangles.
How do you find the perimeter of a regular polygon?
+The perimeter of a regular polygon is equal to the number of sides times the side length.
Related Terms:
- Area Compound shapes worksheet answers
- Composite figures shaded area Worksheet
- Areas of Regular Polygons pdf
