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DochEvi [55]
3 years ago
7

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 th

e 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)
Mathematics
1 answer:
guajiro [1.7K]3 years ago
6 0

Answer:

<h2>The total surface area is 402 square units.</h2>

Step-by-step 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 \times 10 = 60 u^{2}

(Remember that the area of a rectangle is defined as b \times h)

Square face area (bottom):

A_{square}=6 \times 6 = 36 u^{2}

(Remember that the area of a square is l \times l)

Triangular faces area:

A_{triangular}=\frac{1}{2}bh=\frac{1}{2}(6)(10.5) =31.5u^{2}

(Remember that the area of a triangle is \frac{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.

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