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Geometry Challenge: Area, Volume, and Polyhedron Identification

This engaging geometry challenge presents a series of problems focused on calculating areas, volumes, and identifying polyhedra. Work through various level tasks including finding areas of shaded regions using π, determining bases and heights of geometric figures, and identifying characteristics of solids. Tackle problems that require knowledge of trapezoids, parallelograms, circles, and polyhedra. Hone your skills in mathematical reasoning and geometry as you solve these step-by-step challenges!

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Geometry Challenge: Area, Volume, and Polyhedron Identification

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  1. Jeopardy

  2. 100 Find the area.

  3. 200 Find the area of the shaded region. Use 3.14 for π.

  4. 300 Find the area of the shaded region. Use 3.14 for π.

  5. 400 Find the area of the shaded region.

  6. 500 A square with a perimeter of 16 inches is inscribed in a circle. What is the area not occupied by the square? (Hint: Find the diameter of the circle by using a special right triangle.) Use 3.14 for π.

  7. 100 A parallelogram has an area of 92 square units. Its height is 4 units. Find the base.

  8. 200 A trapezoid has an area of 105 square units. Its bases are 12 units and 18 units. Find the height.

  9. 300 The St. Peter’s Basilica dome in Rome, Italy could cover a ground area of 1365 square meters. Find the diameter of the dome. Use 3.14 for π.

  10. 400 Write and solve an equation to find the radius of the circle given its circumference C. Use the radius to find the area of the circle. Use 3.14 for π. C = 94.2 m

  11. 500 A trapezoid has an area of 90 square units. It has a base of 4 units and a height of 9 units. Find the other base.

  12. 100 Identify the solid and tell whether it is a polyhedron.

  13. 200 Identify the solid and tell whether it is a polyhedron.

  14. 300 Identify whether the solid is a polyhedron. Then say how many faces, edges, and vertices it has.

  15. 400 Identify whether the solid is a polyhedron. Then say how many faces, edges, and vertices it has.

  16. 500 Identify whether the solid is a polyhedron. Then say how many faces, edges, and vertices it has.

  17. 100 Find the surface area.

  18. 200 Find the surface area.

  19. 300 Find the surface area.

  20. 400 Find the surface area.

  21. 500 Find the surface area.

  22. 100 Find the volume.

  23. 200 Find the volume.

  24. 300 Find the volume.

  25. 400 Find the volume.

  26. 500 Find the volume.

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