will give medal and fan!(:

Question

anonymous · Answer

attachment

whpalmer4 · Answer

The surface area of the prism is the area of the 2 ends (triangles), the bottom, the back edge, and the sloping face.  The area of a triangle is given by $$A=\frac{1}2bh$$ and the area of a rectangle (all the other sides) is given by $$A=lw$$
Look at your diagram, spot the dimensions of the various sides, compute their areas, and add them up.

anonymous · Answer

Oh! I got 24?

whpalmer4 · Answer

For the remaining edge of the triangle (the hypotenuse) you can use the Pythagorean theorem, $a^2+b^c=c^2$ — the sides you know are $a$ and $b$.

whpalmer4 · Answer

That seems improbably low, given that the thing is 19 long!

whpalmer4 · Answer

Let's work through it.  The triangle has sides 6 and 8, and we need to find the hypotenuse.  What do you get for that?

anonymous · Answer

64

whpalmer4 · Answer

Nope.  $$a = 6, a^2 = ?$$

anonymous · Answer

36

whpalmer4 · Answer

Right!  $$b = 8, b^2=?$$

anonymous · Answer

36 and 64

whpalmer4 · Answer

Right.  Add those together and you get?

anonymous · Answer

100

anonymous · Answer

@whpalmer4 ?

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

Sorry, my web browser is misbehaving...

Yes, 100 is correct.  What is the square root of 100?  That is the length of the side of the triangle we don't yet know.

anonymous · Answer

it's alright.

10

whpalmer4 · Answer

Okay, can you find the area of the triangle for me?

anonymous · Answer

how do i do that

whpalmer4 · Answer

I gave you the formula up above...

anonymous · Answer

i dont know :(

anonymous · Answer

were trying to find the surface area

whpalmer4 · Answer

Right.  The surface area is the sum of the area of all of the shapes that make up the surface.  The formula for the area of a triangle was the first thing I gave you.

whpalmer4 · Answer

Can you identify which sides we will use to find the area, if we need the base and the height?

anonymous · Answer

100 and 19?

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

No, 100 isn't the length of a side of the triangle.  Remember, no side of a triangle can be greater than the sum of the other two sides!

whpalmer4 · Answer

10 is the length of the hypotenuse...

whpalmer4 · Answer

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whpalmer4 · Answer

Which one is the height, and which one is the base?

whpalmer4 · Answer

The height is always at right angles to the base...

anonymous · Answer

6 and 8??

whpalmer4 · Answer

Right!  So what is the area of the triangle that makes up the end of the prism?

anonymous · Answer

14 ?

whpalmer4 · Answer

How did you arrive at that result?

anonymous · Answer

@whpalmer4 cause i added 6 and 8?

whpalmer4 · Answer

The formula is $$A = \frac{1}{2}bh$$Why did you add $b+h$?

whpalmer4 · Answer

You need to multiply them, and then divide by 2.  Or you could save a step later and skip the dividing by 2, because we have 2 of those triangles!

anonymous · Answer

okay so when i multiple them i get 48 then so i just divide by 2?

whpalmer4 · Answer

Right.  The area of each triangle is 24. 

Now let's find the area of bottom of the prism.  Looking at my diagram, can you tell me the length and width?

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