Question

Find the area of parallelogram ABCD given m A = 30 and the following measures. AB = 10 in.; AD = 6 in.

Answer 1

Is there a figure?

Answer 2

No

Answer 3

Ok, now there is a figure.

Answer 4

Okay

Answer 5

Notice that the figure I drew is according to the given info. We have angle A of 30 degrees, and the two sides with the given lengths.

Answer 6

Do you know how to find the area of a parallelogram?

Answer 7

Yes

Answer 8

What is the formula?

Answer 9

Base x Altitude

Answer 10

Correct.
We can use 10 in. as the base.
We need to find the altitude.

Answer 11

We are given the measure of angle A in order to be able to calculate the altitude.

Answer 12

The altitude is perpendicular to two opposite sides.
We need to find h.
Are you learning sine, cosine, tangent?

Answer 13

Haven't used them. Not learning them

Answer 14

Ok. Have you learned the ratios of the lengths of the sides of the 30-60-90 triangle?

Answer 15

No

Answer 16

If you have not learned the 30-60-90 triangle or the trig ratios, then you can't solve this problem. What section in your studies is this problem from?

Answer 17

Area of Parallelograms

Answer 18

Do they give you an example similar to this problem where they want the area, but they don't give you the altitude?

Answer 19

Do they give you an example where they show you how you can use find the altitude given the length of a side and the measure of an angle?

Answer 20

Two other problems without drawn figures

Answer 21

Not having a figure is not a problem, because with the given info, we were able to come up with a figure.

Answer 22

I can only find the altitude using a 30-60-90 triangle or trigonometry.
If you haven't learned either of those two things, I don't see how you can be expected to find the altitude.

Answer 23

It's an online class and I'm basically teaching myself all of this. I haven't learned 30-60-90, because, I was not assigned that lesson.

Answer 24

Thanks for the help, anyhow.

Answer 25

Ok.
I tell you what, I'll teach you the 30-60-90 triangle, then we will continue with this problem.

Answer 26

In a right triangle, whose angle measures are 30, 60, and 90 degrees, the sides havbe these ratios of lengths.



\(1~~:~~\sqrt 3~~:~~2\)

Answer 27

This is simpler than it seems.
The triangle has two sides called legs. Those sides form the right angle.
The longest side is the side opposite the right angle. This side is called the hypotenuse.

Answer 28

The ratio of the lengths of the sides above is in the order:

short leg : long leg : hypotenuse

The short leg is the shortest side of the triangle.
The long leg ins the next longer side.
The hypotenuse is the longest side of the triangle.

Answer 29

What the ratio tells you is that the hypotenuse is twice the length of the short leg.
The long leg is \(\sqrt 3\) times the length of the short leg.

Answer 30

Now let's go back to your problem.
Let's just look at the triangle on the left side, so we can find the altitude of the parallelogram.

Answer 31

Okay

Answer 32

We need h.
In the triangle above, h is the leg opposite the 30 deg angle, so h is the short leg.
Remember from the ratios above for a 30--60-90 triangle, that the hypotenuse is twice the length of the short leg.
Side AD is the hypotenuse, and h is the short leg.
Since AD is twice h, then h is half of AD.
What is half of 6 in.?