Question

The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to cover the block entirely with paper. How much paper do you need?

Answer 1

Total paper required = 165 cm²

Explanation:

Paper required to cover the entire block = (Surface area of the prism at the base - area of the top of the prism) + Lateral surface area of the pyramid

Surface area of the rectangular prism = 2(lb + bh + hl)

(here l, b, h are the length, width and height respectively)

= 2(5×5 + 5×4 + 4×5)

= 2(25 + 20 + 20)

= 2×65

= 130 cm²

Area of the top of the prism = (side)²

= 5²

= 25 cm²

Lateral area of the square pyramid = 4 × Area of one lateral side

= 4 ×
`[(1)/(2)(\text{Base})(\text{Height})]`

= 4 ×
`[(1)/(2)(5)(6)]`

= 60 cm²

Total paper required = (130 - 25) + 60

= 105 + 60

= 165 cm²