Question

Find the area .

Answer 1

Well, I have a way I think this could be solved.

Answer 2

okay

Answer 3

Alright, so the area of a triangle is?

Answer 4

The formula, I mean.

Answer 5

You multiply the b * h and then divide by 2.

Answer 6

Or, 1/2bh, yes. So we know that the base of the shaded region is...?

Answer 7

4

Answer 8

Yes. So this is where the "I think" comes in. I believe that the height here is that slanted region, or the hypotenuse of the right triangle. How do you find that third side do you think?

Answer 9

Hm I don't know.

Answer 10

Multiply something? I don't know

Answer 11

Heard of Pythagorean Theorem?

Answer 12

Yes.

Answer 13

Do you know how to use it?

Answer 14

I'm not sure which numbers would be the a^2 + b^2 = c^2

Answer 15

Generally the hypotenuse is c^2, as far as a^2 and b^2 it honestly doesn't matter. So, what is the value of c here?

Answer 16

It would be 80?

Answer 17

No.
\[8^2+5^2=c^2\]
\[64+25=c^2\]
\[89=c^2\]
\[\sqrt{89} = c\]

Answer 18

\[\frac{ 1 }{ 2 } \times 4 \times \sqrt{89} = area\]

Answer 19

Just plug that into your calculator and, in theory, it will be the area. I honestly don't know what the height would be if it isn't that hypotenuse there.

Answer 20

So I wasn't supposed to do the shaded part then? Okay that makes sense when broken down like that. Thank you very much :)

Answer 21

No, that is the shaded area. We just had to use the other triangle to get the hypotenuse which should be the height.

Answer 22

Um wait hold on...

Answer 23

square root of 89?

Answer 24

Okay nvm.

Answer 25

Orrrr there's another way we could have and I think should have done this

Answer 26

find the hypotenuse with a = 8, b = 5
find the hypotenuse with a = 8, b = 9
now find the area with the values.
and subtract smaller from the higher

Answer 27

Heh. Yeah, that's why I wasn't sure about the slant. Yeah, exactly what @sangya21 said

Answer 28

I was looking at it and I was kind of iffy about it. But sangya there is exactly right

Answer 29

okay i'm a little confused again.

Answer 30

So you see how the lower part is 5+4? That makes a big triangle. You have to find the area for both triangles and then subtract them.

Answer 31

yes

Answer 32

You don't even need to find the hypotenuse

Answer 33

Find AC
Then Find AD

Answer 34

\[\frac{ 1 }{ 2 }bh\]
\[\frac{ 1 }{ 2 }(9)(8)\]
\[\frac{ 1 }{ 2 }(5)(8)\]

\[\frac{ 1 }{ 2 }(9)(8) - \frac{ 1 }{ 2 }(5)(8)\]

This will get you the area of the smaller triangle.

Answer 35

When you take the big area, and you subtract the little area (the part I scribbled out) you're left with the area you need.