Question

An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. The area of the trapezoid is

Answer 1

hi

Answer 2

hey sup shadow

Answer 3

Let me draw this bad boy

Answer 4

The area of a trapezoid is found using the following formula:
\[A_{t} = \frac{ a+ b }{ 2 }h\]

Answer 5

a is 8, b is 14

Answer 6

We need h, or the height of the trapezoid

Answer 7

Are you familiar with trigonometry, or Sin/Cos/Tan?

Answer 8

not at all

Answer 9

Oi

Answer 10

Well it's a way of dealing with triangles. Pretty sure it's the easiest way to solve this, so I don't know why you'd get this problem without having learned it xd

Answer 11

We draw a line and see our triangle take shape. Notice that the height of the triangle is the height of the trapezoid.

Answer 12

33 sq. units
33√2 sq. units
72 sq. units
da answer choices i forgot to put earlier

Answer 13

There's an acronym for Sin/Cos/Tan that goes, SOH CAH TOA

It stands for Sine = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

Answer 14

We'll use tan to look at the height of the triangle (opposite to the 45 degree angle), and the base of the triangle (adjacent to the 45).

Answer 15

We find the base by subtracting 8 from 14

Getting this area ->

Answer 16

\[\tan 45 = \frac{ x }{ 6 }\]

Answer 17

Or we could use big brain and realize that an isosceles triangle is a triangle with two equal sides. Lol

Answer 18

So the base of the triangle is the same length as the height of the triangle. You don't need trig identities.

Answer 19

That's just not graphically depicted in what I drew. Sorry, no sleeps :P

Answer 20

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Shadow
The area of a trapezoid is found using the following formula:
\[A_{t} = \frac{ a+ b }{ 2 }h\]
\(\color{#0cbb34}{\text{End of Quote}}\)

a is 8, b is 14, h is 6

Answer 21

Input and you get your answer.

Answer 22

@uhfinn you followed all that?

Answer 23

Hmm actually, that doesn't come out right.

Answer 24

yea i ddidnt get da right answer

Answer 25

I got it don't worry

Answer 26

So I forgot that there's two triangles in our trapezoid lol

Answer 27

This is why for geometry problems, it's helpful to draw it all out.

Answer 28

So to get the base of one side triangle of a trapezoid, do (bottom - top)/2

Answer 29

Input that new height and you should be good

Answer 30

ok got it thank you shadow ur so cool and awesome ur awesome thanks

Answer 31

np