Question

Find the surface area to the nearest whole number

Answer 1

The surface area is
`180\ m^(2)`

Explanation:

we know that

The surface area of the composite figure is equal to the area of its four lateral triangular faces of the pyramid in the top plus the lateral area of the prism plus the area of the base of the prism

so

`SA=4[(1)/(2)(4)(l)]+(4+4+4+4)(8)+4^(2)`

`SA=8l+144`

Find the slant height (l) of the pyramid

Applying the Pythagoras Theorem

`l^(2)=(b/2)^(2)+h^(2)`

we have

`b=4\ m`

`h=4\ m`

substitute

`l^(2)=(4/2)^(2)+4^(2)`

`l^(2)=20`

`l=√(20)\ m`

Find the surface area

`SA=8l+144`

`SA=8(√(20))+144=180\ m^(2)`