Question

4.2

The solid was created by connecting two congruent square pyramids to a rectangular prism.


18 in


x


15


1


15 in.


What is the surface area of this solid?


square inches

Answer 1

The answer is "
`\bold{1920 \ in^2}`".

Explanation:

Please find the graph file.

Rectangular solid area:

Its region comprises four rectangles, each 15 for each case 14 in each.

The rectangle field is the formula
`A = lw`

The four rectangles are therefore covered by a zone:
`\to A = 4lw = 4 * 15 \ in * 14 \ in = 840 \ in^2.`

square Pyramids area:

The pyramids in both squares have 8 triangular facets.

Each triangle has a 15-inch basis with a 14-inch base.

The triangle zone formulation is
`A = (1)/(2)bh`

That's it. The 8 triangles area is
`\to A = 8 * (1)/(2)bh = 4bh = 4 * 15 \ in * 18 \ in = 1080 \ in^2`

Total field surface:

Strong rectangular
`= 840 \ in^2`

Pyramids in the Square
`= 1080`

Overall area
`= 1920 \ in^2`

The number is
`1920\ in^2` for a total area.