Question

Stuck on these two shapes
need help in working out the surface area​

Answer 1

Part 1) The surface area of the triangular prism is
`SA=660\ cm^(2)`

Part 2) The surface area of the trapezoidal prism is
`SA=2,864\ cm^(2)`

Explanation:

Part 1) Find the surface area of the triangular prism

we know that

The surface area is equal to

`SA=2B+PL`

where

B is the area of the triangular base of the prism

P is the perimeter of the base of the prism

L is the length of the prism

Find the area of the triangular base B

`B=(1)/(2)(10)(12)=60\ cm^(2)`

Find the perimeter of the base P

`P=10+13+13=36\ cm`

`L=15\ cm`

substitute the values

`SA=2(60)+(36)(15)=660\ cm^(2)`

Part 2) Find the surface area of the trapezoidal prism

we know that

The surface area is equal to

`SA=2B+PL`

where

B is the area of the trapezoid base of the prism

P is the perimeter of the base of the prism

L is the length of the prism

Find the area of the trapezoid base B

`B=(1)/(2)(28+15)(8)=172\ cm^(2)`

Find the perimeter of the base P

`P=15+28+10+10=63\ cm`

`L=40\ cm`

substitute the values

`SA=2(172)+(63)(40)=2,864\ cm^(2)`