Question

Find the surface area of this triangular prism.

Please explain as well, I’m struggling with it.

Answer 1

84
`cm^(2)`

Explanation:

To find the surface area of a prism, one will have to find the area of each of the sides of the prism, then add the areas up. First, find the dimensions of each of the sides

Front; 5 x 6

Front triangle; 3 x 4

Back triangle; 3 x 4

Bottom; 4 x 6

Back; 3 x 6

The front is a rectangle, hence one has to
`base * height` to find the area;

5 x 6

= 30

The front triangle is a triangle, hence on has to do
`(base * height)/(2)` to find the area;

`(3*4)/(2)`

= 6

The back triangle is a triangle, hence on has to do
`(base * height)/(2)` to find the area;

`(3*4)/(2)`

= 6

The back is a rectangle, so one has to do
`base * height` to find the area;

4 * 6

= 24

The bottom is a rectangle, o one has to do
`base * height` to find the area;

3 * 6

= 18

Noe one has to add up all the areas to find the total surface area;

Front + Front_triangle + Back_triangle + Bottom + Back

30 + 6 + 6 + 24 + 18

= 84

Answer 2

SA= 84 cm^2

Explanation:

So first locate all the surfaces

we got 5 sides in total

Now calculate each one

Lets start with the 2 triangles

so formula for area of triangl is 1/2(b*h)

So in this case it’s 6

Now there are 2 identical triangles

So Times the 6 by 2

You’ll get 12

Thats 2 sides

Now for the side with the rectangle of 5cm and 6cm

Area of rectangle is 5*6=30

That would onay be 1 side

Now for the bottom of the prisim which is the side with 4cm and 6cm

Same rectangle so multiply

4*6=24

Thats another side down

The last side is on the left with the back not visible. The two dimensions are 6 and 3

Now multiply 6*3

18

Now add up your total

18+24+12+30=84

So 84 cm^2 OR 84 square centimeters