Composite Shapes
Break down complex shapes into simpler parts to find area and volume.
Learn
Working with Composite Shapes
A composite shape is made up of two or more simple shapes combined. To find the area or volume:
- Addition method: Break the shape into parts, find each area/volume, then add
- Subtraction method: Start with a larger shape and subtract the missing piece
- Identify shapes: Look for rectangles, triangles, circles, and semicircles
- Be systematic: Label dimensions and work step by step
Practice
Question 1: An L-shaped room has dimensions: main part 10x8 m, extension 4x3 m. Find total area.
Answer
Main: 10 x 8 = 80 m^2. Extension: 4 x 3 = 12 m^2. Total: 80 + 12 = 92 m^2.
Question 2: A rectangle 12x8 has a 3x3 square cut from one corner. Find remaining area.
Answer
Rectangle: 12 x 8 = 96. Square: 3 x 3 = 9. Remaining: 96 - 9 = 87 square units.
Question 3: A shape is made of a rectangle 6x4 with a semicircle (diameter 4) on one end. Find total area. (pi = 3.14)
Answer
Rectangle: 6 x 4 = 24. Semicircle: (1/2)(3.14)(2^2) = 6.28. Total: 24 + 6.28 = 30.28 square units.
Question 4: Two cubes, one 3 cm and one 2 cm on edge, are glued together. Find total volume.
Answer
Cube 1: 3^3 = 27 cm^3. Cube 2: 2^3 = 8 cm^3. Total: 27 + 8 = 35 cm^3.
Question 5: A T-shaped figure has a top bar 8x2 and a stem 2x5. Find total area.
Answer
Top: 8 x 2 = 16. Stem: 2 x 5 = 10. Total: 16 + 10 = 26 square units.
Question 6: A pool is rectangular (15x10 m) with a semicircular end (diameter 10 m). Find total area. (pi = 3.14)
Answer
Rectangle: 15 x 10 = 150 m^2. Semicircle: (1/2)(3.14)(5^2) = 39.25 m^2. Total: 189.25 m^2.
Question 7: A rectangular prism 8x6x4 has a smaller prism 2x2x4 cut out. Find remaining volume.
Answer
Large: 8 x 6 x 4 = 192. Small: 2 x 2 x 4 = 16. Remaining: 192 - 16 = 176 cubic units.
Question 8: An arrow shape is a 5x5 square with a triangle (base 5, height 3) on top. Find total area.
Answer
Square: 5 x 5 = 25. Triangle: (1/2)(5)(3) = 7.5. Total: 25 + 7.5 = 32.5 square units.
Question 9: A figure is made of two rectangles: 10x4 and 6x3 overlapping by a 2x3 region. Find total area.
Answer
Rect 1: 40. Rect 2: 18. Overlap: 6. Total: 40 + 18 - 6 = 52 square units.
Question 10: A cylinder (r=3, h=10) sits on top of a rectangular prism (6x6x5). Find total volume. (pi = 3.14)
Answer
Cylinder: 3.14 x 9 x 10 = 282.6. Prism: 6 x 6 x 5 = 180. Total: 282.6 + 180 = 462.6 cubic units.