Question

Find the area of each figure. When an answer is NOT a whole number, round to the nearest tenth.

Answer 1

@surjithayer

Answer 2

@timo86m @whpalmer4

Answer 3

The 45º-45º should give you a clue about the triangle given. Does that ring a bell?

Answer 4

Here's another hint: in a right triangle, one of the sides going into the right angle will serve as an altitude or height. The other will serve as a base. Area of a triangle is \[A = \frac{1}{2}bh\] where \(b\) is the length of the base, and \(h\) is the height or altitude

Answer 5

is 14 * sqrt 2 the base or height

Answer 6

Does the side labeled with that go into the little right triangle angle box?

Answer 7

Has anyone ever pointed out to you that in a 45/45/90 triangle, such as the one we have here, the hypotenuse is always \(\sqrt{2}\) times the length of either of the two sides?

Answer 8

what if the their isn't sides

Answer 9

14 * sqrt 2 * sqrt 2 = 56m^2 <--- ha ha I think that's wrong! :D

Answer 10

how can you have a triangle without sides?

Answer 11

that's what my problem is

Answer 12

okay, that's a right triangle, and you know the length of the hypotenuse, and it's not just any right triangle, it's an isosceles triangle because the two angles are equal. What does that imply about the lengths of the unknown sides?

Answer 13

Come on, man, you've done a number of problems like this now, aren't you picking up on the patterns?

Answer 14

I got 56m^2

Answer 15

show me your work

Answer 16

\[14\sqrt{2} * \sqrt{2} = 28m^2\]
not 56m^2

Answer 17

Where did you get those numbers?

Answer 18

from the figure where else duh

Answer 19

14 * sqrt 2 * sqrt 2 <--- as the hypotenuse = 28m^2

Answer 20

can you please go read what I wrote earlier about the base and the height?

Answer 21

yes, but there are no sides though HELLO??? How else will I solve it

Answer 22

duh. it's an isosceles triangle. use the Pythagorean theorem.

Answer 23

I did Pythagorean Theorem and I got sqrt 14.
a & b = x c = 14 times sqrt 2

Answer 24

\[c = 14\sqrt{2}\]\[c^2=\]?

Answer 25

wait stop right there where a & b

Answer 26

no need for a and b. I told you what c is. What is the value of c^2?

Answer 27

c*c

Answer 28

28

Answer 29

\[14\sqrt{2}*14\sqrt{2} = 28\]?!?

Answer 30

\[\sqrt{2} \approx 1.414\]\[14*1.414\approx 20\]\[20*20 = 400\]
Missed it by a county mile!

Answer 31

explain how you got that answer

Answer 32

what is \[\sqrt{2}*\sqrt{2}\]?

Answer 33

How is 14\[14\sqrt2 * 14\sqrt2 = 28 ---> 392\]

Answer 34

I got 392 not 28 if you multiplied 14 * sqrt 2 twice

Answer 35

Yes, c^2 = 392.

Now, we know (at least I do) that a = b because this is an isosceles triangle because the two angles other than the right angle are equal. So in the Pythagorean theorem:
\[a^2+b^2=392\]\[a^2+a^2=392\]\[2a^2=392\]Solve for the value of \(a\)

Answer 36

anyways x = 14

Answer 37

is that the height

Answer 38

that is the height, and it is also the base.

Answer 39

why is that?

Answer 40

98m^2

Answer 41

I got 98m^2 is that right

Answer 42

yes. (1/2)*14*14 = 98. if the original measurements are in meters, then m^2 is the right unit.