Question

Another trapezoid problem

Find the area

Answer 1

Heres the pic

Answer 2

Ik how to find the area but im not sure how to find the hypotenuse

Answer 3

@mathstudent55

Answer 4

Good.
Now we get to see what the side ratios are for a 45-45-90 triangle.

Answer 5

In a 45-45-90 triangle, you have a right triangle with two congruent angles.
The sides opposite the 45-deg angles are congruent.
The hypotenuse is longer than those two sides.

Answer 6

We let the two congruent sides equal a.
Now we can find h, the length of the hypotenuse using the Pythagorean theorem.
\(a^2 + a^2 = h^2\)
\(2a^2 = h^2\)
\(h^2 = 2a^2\)
\(h = \sqrt{2a^2} \)
\(h = \sqrt 2 a\)

Answer 7

Now you see that is a 45-45-90 triangle, the two legs are congruent.
They have the same length.
Then the hypotenuse is sqrt2 times longer than the legs.

Answer 8

ok now what? @mathstudent55

Answer 9

Now you know about the 45-45-90 triangle also.

Answer 10

Now let's deal with the trapezoid problem.

Answer 11

ya is the ratio sqrt 2 always for 45 90

Answer 12

For the area of a trapezoid, we need the two bases and the height.

Answer 13

Yes.
The hypotenuse is always sqrt 2 times the legs in a 45-45-90 triangle.

Answer 14

alright got that part