- Problem 1: The cube has sides of 3 cm. Each face is a square with area 3 cm × 3 cm = 9 cm². A cube has 6 faces, so total surface area is 6 × 9 cm² = 54 cm².
- Problem 2: The cube has sides of 4 cm. Each face is a square with area 4 cm × 4 cm = 16 cm². A cube has 6 faces, so total surface area is 6 × 16 cm² = 96 cm².
- Problem 3: The rectangular prism has dimensions 2 ft × 2 ft × 6 ft. It has two 2 ft × 2 ft faces (area 4 ft² each) and four 2 ft × 6 ft faces (area 12 ft² each). Total surface area is (2 × 4 ft²) + (4 × 12 ft²) = 8 ft² + 48 ft² = 56 ft².
- Problem 4: The rectangular prism has dimensions 5 m × 3 m × 10 m. It has two 5 m × 3 m faces (area 15 m² each), two 5 m × 10 m faces (area 50 m² each), and two 3 m × 10 m faces (area 30 m² each). Total surface area is (2 × 15 m²) + (2 × 50 m²) + (2 × 30 m²) = 30 m² + 100 m² + 60 m² = 190 m².
- Problem 5: The square pyramid has a square base of 8 ft × 8 ft and four triangular faces. The base area is 8 ft × 8 ft = 64 ft². Each triangular face has a base of 8 ft and a height of 10 ft, so the area of one triangle is (1/2) × 8 ft × 10 ft = 40 ft². The total area of the four triangles is 4 × 40 ft² = 160 ft². Total surface area is 64 ft² + 160 ft² = 224 ft².
Parent Tip: Review the logic above to help your child master the concept of surface area worksheet printable.
