Question

Find the area of a trapezoid. Leave your answer in simplest radical form.

Answer 1

what's the formula for the area of a trapezoid?

Answer 2

A = (b1 + b2/2)*h

Answer 3

Okay, which of those quantities do you know, and which don't you know?

Answer 4

I know base 1 is 7 and that the height is 5, but I don't know base 2.

Answer 5

Okay. Let's look at the triangles. How about the triangle on the right, can you figure out its dimensions?

Answer 6

Wait, what do you want to know? ...It's embarrassing how bad I am at math.

Answer 7

Well, can you tell me the base and height and angles of that triangle?

Answer 8

Hint for the height: the thing that makes up the height leg is a square...

Answer 9

Like I know that it is isosceles based on the angle measures and they are both 5

Answer 10

Okay, that's good, so what are the two angles (besides the 90 degree one)?

Answer 11

45 and 45

Answer 12

Right. Okay, so we know that it has angles 45, 45, 90, and legs 5, 5, sqrt(50). What about the other triangle?

Answer 13

It's the same

Answer 14

we know that because...

Answer 15

they have congruent angle measures and side lengths?

Answer 16

right! so, now do we have enough information to find the longer base?

Answer 17

Yes

Answer 18

and you say you're bad at math :-)

Answer 19

Ha I am. So what do I use to find it?

Answer 20

well, isn't it the base of the left triangle + the base of the square + the base of the right triangle?

Answer 21

Wow, I am such an idiot. That is really obvious. Thank you.

Answer 22

well, not quite so obvious overall — the diagram doesn't make it look like the answer you get, does it?

Answer 23

whenever you see "not to scale", that's often code for "it really looks much different" :-)

Answer 24

True spit. So is it 85?

Answer 25

oh, wait, I did misspeak, the thing in the middle isn't a square, it's a rectangle, but that didn't matter for finding the sides of the triangles...

Answer 26

Ok good haha. Thanks again!

Answer 27

so let's see, the top dimension is 7, the bottom dimension is 5+7+5 = 17, the height is 5, so our area should be 1/2(7+17)*5 = ?

Answer 28

we can check a different way, by adding the areas of the rectangle and two triangles.

rectangle is 5x7 = 35
triangle is 1/2 b h = 1/2 * 5 * 5 = 25/2, we've got 2 of them, so 2 * 25/2 = 25
rectangle + triangles = 35 + 25 = 60

Answer 29

Sweet. I got it right!

Answer 30

what was the 85 you mentioned?

Answer 31

85 cm^2 is the answer

Answer 32

not for the drawing I'm looking at...

Answer 33

The two triangles put together make a 5x5 square, area = 25 cm^2
The rectangle is 5x7 = 35 cm^2
25 + 35 = 60 cm^2 for the whole thing.

Answer 34

Oh. Okay. Thanks!