Question

The lateral area of the right regular triangular prism is 18cm^2. Find the total surface area.Give answer in decimal form rounded of to 2 decimal places.

Answer 1

im looking for the area of the rectangle face and triangle base

Answer 2

This shouldn't be too hard :)
Let's consider just one rectangular face...

Answer 3

You with me?

Answer 4

yes

Answer 5

Now, it'd be much nicer if we knew how long this is:

Answer 6

Which we do, actually... we know that the area is 18...

Answer 7

And the area is equal to the product of the two side-lengths...3 and an unknown number...
So... three times a number is 18, what is that number?

Answer 8

6

Answer 9

That's right :)

Answer 10

how come looking at the picture 3cm looks alot longer then the 6cm side.

Answer 11

These things are rarely drawn to scale.

Answer 12

?

Answer 13

If it bothers you that much, I'll draw a slightly more accurate figure :P

Answer 14

ohhh i see

Answer 15

Okay, that was the easy part, though... ready for the actual 'finding the surface area'?

Answer 16

yes

Answer 17

As you can see, there are three-rectangles around the sides, each with area 18.. so that makes how many total?

Answer 18

??? how many what?

Answer 19

total area around the three rectangles...

Answer 20

54 cm^2

Answer 21

That's right, and that's the total area around the three rectangles, now find the area of one triangular base.

Answer 22

okay one sec

Answer 23

gonna try it right now

Answer 24

Area of an equilateral triangle given a side-length s is
\[\Large A_\Delta=\frac{s^2\sqrt3}{4}\]

Answer 25

idk i got about 7.8

Answer 26

oh ill use the formula u gave me

Answer 27

Yes, please do :P

Answer 28

wait can u draw that formula on the triangle so i can see it? i dont really get it

Answer 29

Well, when you have an equilateral triangle, you know all sides measure the same, right?
So just square the side-length and mutltiply to \(\LARGE \frac{\sqrt3}{4}\)

Answer 30

Howd u get