anonymous
  • anonymous
Find the area & perimeter of the figure
Geometry
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
1 Attachment
mathstudent55
  • mathstudent55
You were given a triangle like this: |dw:1437006808180:dw|
mathstudent55
  • mathstudent55
What do the circled marks mean? |dw:1437006848302:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
@11.seventeen what do the circled marks mean
anonymous
  • anonymous
doesn't it mean its equal
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
Yes. All sides are congruent. That means every side of this triangle measures 2a mm. That makes the perimeter easy to find. What is the perimeter of a triangle?
mathstudent55
  • mathstudent55
\(\Large P_{triangle} = a + b + c\) where a, b, and c are the lengths of the sides of the triangle.
mathstudent55
  • mathstudent55
\(P = 2a + 2a + 2a = 6a\) The perimeter of the triangle is 6a mm
mathstudent55
  • mathstudent55
Ok so far?
anonymous
  • anonymous
Yes. It's the same as what i got @mathstudent55
mathstudent55
  • mathstudent55
Now you have to find the area.
anonymous
  • anonymous
And I would do that how ? Because I don't have the heigh . I have the base is 2
mathstudent55
  • mathstudent55
To find the area, you need to find the height of the triangle since the formula for the area involves the height.
mathstudent55
  • mathstudent55
Have you heard about the ratios of the lengths of the sides of a 30-60-90 triangle?
anonymous
  • anonymous
Yes but I never understood it
mathstudent55
  • mathstudent55
Ok. I'll explain it to you. Here is a triangle with a right angle and a 30-deg angle and a 60-deg angle. |dw:1437011007751:dw|
mathstudent55
  • mathstudent55
Since the right angle is 90 deg, this triangles' three angles have measures 30, 60, and 90 degrees. This is what is called a 30-60-90 triangle.
mathstudent55
  • mathstudent55
In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the short leg. If you call the length of the short leg 1, then the hypotenuse has length 2. |dw:1437011223749:dw|
mathstudent55
  • mathstudent55
The length of the long leg is \(\sqrt 3\) times the length of the short leg.
mathstudent55
  • mathstudent55
|dw:1437011291789:dw|
mathstudent55
  • mathstudent55
So far all we have is that the lengths of the sides of a 30-60-90 triangle are in the ratio of 1 : \(\sqrt 3 : 2\)
mathstudent55
  • mathstudent55
Do you understand so far?
anonymous
  • anonymous
sort of
mathstudent55
  • mathstudent55
It is simpler than you think. Think of \(\sqrt 3\) as being approximately 1.7 All this means is that: In a 30-60-90 triangle, the long leg is 1.7 times the length of the short leg. The hypotenuse is 2 times the length of the short leg.
mathstudent55
  • mathstudent55
If a 30-60-90 triangle has a short leg of 1, then the long leg is 1.7 * 1 = 1.7 the hypotenuse is 2 * 1 = 2
anonymous
  • anonymous
how do I get the height out of this?
mathstudent55
  • mathstudent55
Another example: If a 30-60-90 triangle has a short leg of length 4, then the long leg is 1.7 * 4 = 6.8 and the hypotenuse is 2 * 4 = 8
mathstudent55
  • mathstudent55
Ok. Let's get back to our problem.
mathstudent55
  • mathstudent55
|dw:1437011694076:dw|
mathstudent55
  • mathstudent55
You see our triangle above. Since all sides are congruent, all angles are also congruent. That means all angles measure 60 degrees. Ok?
mathstudent55
  • mathstudent55
|dw:1437011786387:dw|
mathstudent55
  • mathstudent55
We are looking for the length of the height. By drawing the height, we created two new triangles. Notice each small triangle is a 30-60-90 triangle.
mathstudent55
  • mathstudent55
|dw:1437011853170:dw|
mathstudent55
  • mathstudent55
Look at the figure above. Each of the two small triangles is a 30-60-90 triangle. The 30 degree angle is above. Since the side of the large triangle has length 2a, half of that is just a, and that is the length of the short side of the 30-60-90 triangle.
mathstudent55
  • mathstudent55
Look at the small triangle in the circle and ignore the rest. |dw:1437012005959:dw|
mathstudent55
  • mathstudent55
The short leg has length a. The long leg has length \(\sqrt 3\) times a, which is simply: \(\sqrt 3 a\) |dw:1437012059638:dw|
mathstudent55
  • mathstudent55
|dw:1437012157126:dw|
mathstudent55
  • mathstudent55
The long leg of the small triangle is the height of the large triangle. That was the height we needed for the area.
mathstudent55
  • mathstudent55
|dw:1437012211126:dw|
anonymous
  • anonymous
so is the height 3a?
mathstudent55
  • mathstudent55
Now we have all the info we need to find the area of the large triangle.
mathstudent55
  • mathstudent55
The height is \(\sqrt 3 a\), not 3a. \(\Large A_{triangle} = \dfrac{bh}{2} \)
mathstudent55
  • mathstudent55
\(\Large A = \dfrac{(a)(\sqrt 3 a)}{2} = \dfrac{\sqrt 3}{2}a^2 ~mm^2\)
anonymous
  • anonymous
thanks!!!
mathstudent55
  • mathstudent55
You're welcome.

Looking for something else?

Not the answer you are looking for? Search for more explanations.