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Geometry Teaching Examples with Solutions

Explore various geometry problems and solutions, including rectangles, triangles, circles, boxes, spheres, cylinders, and cones. Learn how to calculate perimeter, area, volume, and surface area using formulas and examples.

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Geometry Teaching Examples with Solutions

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  1. Chapter R.1 Formulas from Geometry

  2. Teaching Example 1 The length of a rectangle is 1 inch less than twice the width. If the width is x inches, write expressions that give the perimeter and area. Solution If the width is x inches, then the length is 2x − 1.

  3. Teaching Example 1 (continued)

  4. Teaching Example 2 Find the area of the triangle. Solution The legs of the right triangle are the base and the height of the triangle.

  5. Teaching Example 3 A circle has a radius of 5 feet. Approximate its circumference and area. Solution

  6. Teaching Example 4 Find the perimeter of a right triangle with one leg of length 11 inches and hypotenuse of length 61 inches. Solution

  7. Teaching Example 4 (continued) Using the Pythagorean theorem, we have The perimeter of the triangle is

  8. Teaching Example 5 The box has dimensions x by 3x by 2y. Find its volume and surface area. Solution

  9. Teaching Example 5 (continued) The area of the top and the bottom is 6x2 square units. The area of the front and the back is 4xy square units. The area of the left and right sides is 12xy square units. The total surface area is 6x2 + 16xy square units.

  10. Teaching Example 6 Estimate, to the nearest tenth, the volume and surface area of a sphere with a radius of 2.3 feet. Solution

  11. Teaching Example 7 A cylinder has radius r = 5 inches and heighth = 3 feet. Find its volume and total surface area to the nearest tenth. Solution Begin by changing 3 feet to 36 inches so that all units are in inches.

  12. Teaching Example 8 Approximate, to the nearest tenth, the volume and surface area (side only) of a cone with a radius of 1.5 inches and a height of 3.5 inches. Solution

  13. Teaching Example 9 Use the fact that triangles ABC and DEF are similar to find the value of x. Solution

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