Question

The diagram below shows a pyramid glued to a the top of a cube.Given that the slant height of the pyramid is 5.9 centimeters,

Find the total surface area of the solid rounded to the nearest square centimeter.
Plz help. Answer quick.

Answer 1

The total surface area is
`251\ cm^(2)`

Explanation:

we know that

The total surface area of the composite figure is equal to the lateral area of the pyramid plus the lateral area of the cube plus the area of the base of the cube

The lateral area of the pyramid is equal to the area of the four lateral triangular faces of the pyramid

The lateral area of the cube is equal to the area of the four lateral square faces of the cube

so

`SA=4[(1)/(2)(b)(h)]+4(b^(2))+b^(2)`

we have that

`b=6\ cm`

`h=5.9\ cm`

substitute

`SA=4[(1)/(2)(6)(5.9)]+4(6^(2))+6^(2)`

`SA=70.8+144+36`

`SA=250.8\ cm^(2)`

Round to the nearest square centimeters

`250.8=251\ cm^(2)`