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? Find it in cm squared.

Answer 1

Hence required paper for entire shape will be L[L+2(2H+H1)] Sq.cm

Explanation:

Given:

A block with rectangular prism at bottom and square pyramid at top.

To Find:

Paper required to cover whole block

Solution:

We know that block consist of two different shapes as prism and pyramid.

So paper covering will be for surface.

hence we required surface area for rectangular prism and square pyramid.

(Refer the attachment)

Now only outer surface should be consider in order to cover the shape.

for square pyramid its length and breadth will be the same .

let L be length and B be breadth and h be height

So total no.of faces will be 6 but on top there is prism placed so top surface will be neglected for the calculations.

Hence No.of faces will be 5.

So total surface area for square pyramid will be

=L*W+2(L*H+W*H)

Here L=W as it is square pyramid

=L^2+4(L*H)

Now for the Prism surface it will have 4 triangles placed on with base as length of pyramid(as shown in fig) and height be H1

So Total area for Prism will be

=4( Area of triangles)

=4*1/2*base*height)

=2*base *height

=2*L*H1

So required Paper will be

Total surface area=Surface are of pyramid+ Area of 4 triangles.

=L^2+4(L*H)+2*L*H1

=L[L+2(2H+H1)].