Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 4 Surface Area of Solids

Total surface area of a square pyramid

Answer: 384 cm²

💡 What it's asking: We need the area of every outside face of a square-based pyramid. It has one square base and four equal triangles, so add their areas.

1. 1Find the square base: 12 × 12 = 144 cm².
2. 2Find one triangle: ½ × base × face height = ½ × 12 × 10 = 60 cm². (The sheet prints 10m; it should be 10 cm.)
3. 3There are four triangles: 4 × 60 = 240 cm².
4. 4Add the base: 144 + 240 = 384 cm².

✅ The four triangles (240) should be bigger than the base (144) here, because each face is tall; 384 cm² fits that.

Surface area formula for a square pyramid in letters

Answer: x² + 2xh cm²

💡 What it's asking: Same idea as a numbered pyramid, but with letters: base side x and face height h. Add the square base and the four triangles.

1. 1The square base has area x × x = x².
2. 2One triangular face has area ½ × x × h.
3. 3Four faces: 4 × ½ × x × h = 2xh.
4. 4Add them: total surface area = x² + 2xh cm². (The sheet says 'x and y', but the face height is labelled h.)

✅ Put x = 12 and h = 10: 144 + 240 = 384, the same as the numbered pyramid in Q1.