Question

A square-based prism made of clay had dimensions of 6 by 6 by 10. A pyramid was removed from the prism as shown below so that the prism has no top. If the slant height of the pyramid is 10.5 units, the total surface area of the remaining clay solid is _____ square units. (Round answer to nearest whole number)

Answer 1

The total surface area is 402 square units.

Explanation:

Givens

• The dimensions of the square-based prism are 6 by 6 by 10.(
  `l=6`,
  `w=6` and
  `h=10`.
• The slant height of the pyramid is 10.5 units.
• The base of the pyramid matches the top of the square prism, so it's square-based prism.

Remember tha the slant height refers to the height of sided triangles.

Basically, the resulting form 4 rectangular faces, 1 square face, and four triangular faces.

Rectangular face area:

`A_(rectangular)=6 * 10 = 60 u^(2)`

(Remember that the area of a rectangle is defined as
`b * h`)

Square face area (bottom):

`A_(square)=6 * 6 = 36 u^(2)`

(Remember that the area of a square is
`l * l`)

Triangular faces area:

`A_(triangular)=(1)/(2)bh=(1)/(2)(6)(10.5) =31.5u^(2)`

(Remember that the area of a triangle is
`(1)/(2) bh`.

Multiplying by the right number of each type, we have the total surface area of the resulting figure:

`A=4(60)+36+4(31.5)=240+36+126=402 u^(2)`

Therefore, the total surface area is 402 square units.