Grade 6 Geometry: Surface Area

Worked examples

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

1. Example 1

   A rectangular prism is 5 cm long, 5 cm wide, and 9 cm tall. Unfold it into a net of 6 rectangles. What is its total surface area in square centimeters?

   1. The net has 3 pairs of matching rectangles.
   2. Top and bottom: 2 × (5 × 5) = 50.
   3. Front and back: 2 × (5 × 9) = 90.
   4. Left and right: 2 × (5 × 9) = 90.
   5. Add them: 50 + 90 + 90 = 230. The surface area is 230 square centimeters.

   Answer: 230

2. Example 2

   A cube has edges of 6 ft. What is its surface area in square feet?

   1. A cube has 6 faces, and each face is a square with sides of 6 feet.
   2. One face: 6 × 6 = 36.
   3. Six faces: 6 × 36 = 216. The surface area is 216 square feet.

   Answer: 216

3. Example 3

   A square pyramid has a square base with sides of 10 cm. Each of its 4 triangle faces has a base of 10 cm and a height of 7 cm. What is its total surface area in square centimeters?

   1. Square base: 10 × 10 = 100.
   2. One triangle face: ½ × 10 × 7 = 35.
   3. Four triangle faces: 4 × 35 = 140.
   4. Add the base: 100 + 140 = 240. The surface area is 240 square centimeters.

   Answer: 240