Answer:
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
