Grade 6 Geometry: Unit Review

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A square pyramid has a square base with sides of 7 cm. Each of its 4 triangle faces has a base of 7 cm and a height of 15 cm. What is its total surface area in square centimeters?

   1. Square base: 7 × 7 = 49.
   2. One triangle face: ½ × 7 × 15 = 52.5.
   3. Four triangle faces: 4 × 52.5 = 210.
   4. Add the base: 49 + 210 = 259. The surface area is 259 square centimeters.

   Answer: 259

2. Example 2

   A rectangular prism is 3 ft long, 4 ft wide, and 2 ft tall. Unfold it into a net of 6 rectangles. What is its total surface area in square feet?

   1. The net has 3 pairs of matching rectangles.
   2. Top and bottom: 2 × (3 × 4) = 24.
   3. Front and back: 2 × (3 × 2) = 12.
   4. Left and right: 2 × (4 × 2) = 16.
   5. Add them: 24 + 12 + 16 = 52. The surface area is 52 square feet.

   Answer: 52

3. Example 3

   A triangle has an area of 30 square inches and a base of 10 in. What is its height in inches?

   1. Area = ½ × base × height, so base × height = 2 × area = 2 × 30 = 60.
   2. Divide by the base: 60 ÷ 10 = 6.
   3. Check: ½ × 10 × 6 = 30. The height is 6 inches.

   Answer: 6