Question

What is the surface area of the figure shown? Plz answer asap

300 cm 2
336 cm 2
264 cm 2
358 cm 2

Answer 1

`264\ cm^(2)`

Explanation:

we know that

The surface area of the figure is equal to the lateral face of the triangular pyramid plus the lateral face of the rectangular prism plus the area of the base of the rectangular prism

step 1

Find the lateral face of the triangular prism

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

`LA=4((1)/(2)(6)(7))=84\ cm^(2)`

step 2

Find the lateral area of the rectangular prism

The lateral area is equal to the perimeter of the base multiplied by the height

`LA=(4)(6)(6)=144\ cm^(2)`

step 3

Find the area of the base of the rectangular prism

`B=(6)(6)=36\ cm^(2)`

step 4

Find the surface area

`84\ cm^(2)+144\ cm^(2)+36\ cm^(2)=264\ cm^(2)`