Find the area & perimeter of the figure

Question

anonymous · Answer

attachment

mathstudent55 · Answer

You were given a triangle like this:
|dw:1437006808180:dw|

mathstudent55 · Answer

What do the circled marks mean?
|dw:1437006848302:dw|

anonymous · Answer

@11.seventeen what do the circled marks mean

anonymous · Answer

doesn't it mean its equal

anonymous · Answer

@mathstudent55

mathstudent55 · Answer

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 · Answer

$\Large P_{triangle} = a + b + c$

where a, b, and c are the lengths of the sides of the triangle.

mathstudent55 · Answer

$P = 2a + 2a + 2a = 6a$

The perimeter of the triangle is 6a mm

mathstudent55 · Answer

Ok so far?

anonymous · Answer

Yes. It's the same as what i got @mathstudent55

mathstudent55 · Answer

Now you have to find the area.

anonymous · Answer

And I would do that how ? Because I don't have the heigh . I have the base is 2

mathstudent55 · Answer

To find the area, you need to find the height of the triangle since the formula for the area involves the height.

mathstudent55 · Answer

Have you heard about the ratios of the lengths of the sides of a 30-60-90 triangle?

anonymous · Answer

Yes but I never understood it

mathstudent55 · Answer

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 · Answer

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 · Answer

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 · Answer

The length of the long leg is $\sqrt 3$ times the length of the short leg.

mathstudent55 · Answer

|dw:1437011291789:dw|

mathstudent55 · Answer

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 · Answer

Do you understand so far?

anonymous · Answer

sort of

mathstudent55 · Answer

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 · Answer

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 · Answer

how do I get the height out of this?

mathstudent55 · Answer

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 · Answer

Ok. Let's get back to our problem.

mathstudent55 · Answer

|dw:1437011694076:dw|