A square-based prism made of clay had dimensions of 6 by 6 by 10. A pyramid was removed from the prism so the prism has no top. what is the total surface area of the remaining clay solid if the slant height of the pyramid is 10.5

Step-by-step explanation:

Given that,

The square based prism has  dimensions is

6 by 6 by 10

Length = 6

Width = 6

Height = 10

Slant height of pyramid is given as

h = 10.6

Note: The base of the pyramid matches the top of the square prism, so it's square-based prism.

So, we are going to have

4 rectangular faces(i.e the square Base prism rectangular faces)

1 square face ( the based of the prism)

four triangular faces( the top pyramid)

So, area of the four face

It is a rectangular shape and it is calculated using

A = length × Breadth

Area of one face is

A = L × W

A = 6 × 10 = 60 Square units

And there are 4 similar rectangle

So, area of the four rectangles is

A' = 4 × 60 = 240 square unit

Now, area of the square base below can be calculated using

A = s²

A" = L² = 6² = 36 Square units

Now, area of the four triangle pyramid at the top

Area of triangle is given as

A = ½bh

A = ½ × 6 × 10.6

A = 31.8 square units.

The area of the four triangles becomes

A"' = 4 × 31.8

A"' = 126 square units

Then, the total area of the shape is

A(total ) = A' + A" + A"'

A(total) = 240 + 36 + 126

A(total) = 402 Square units

So, the total area of the solid shape is 402 Square units