ISEE upper Level Math help » Geometry » airplane Geometry » triangle » Equilateral triangle

For an equilateral triangle, side A actions

*
 and side B actions
*
. What is the length of side A?


Explanation:

First you must recognize that for an it is provided triangle, every 3 sides have equal lengths.

You are watching: What is the angle of an equilateral triangle

This means you can set the 2 values because that Side A and Side B equal to one another, because they measure up the very same length, to settle for 

*
.

*

*

*

*

You now understand that 

*
, yet this is not your answer. The inquiry asked for the length of next A, therefore you must plug 3 right into that equation.

*

*

*

So the length of next A (and side B for the matter) is 8.

 


One angle of an it is intended triangle is 60 degrees. One side of that triangle is 12 centimeters. What are the procedures of the two other angles and also two various other sides?


Explanation:

An it is provided triangle is one in i m sorry all 3 sides room congruent. It additionally has the home that all three internal angles room equal. In other words, all three angles that an equilateral triangle are constantly 60°. Since all sides room congruent, the other two sides both measure up 12 centimeters.


*


*


*


*


Explanation:

To discover the perimeter of an it is provided triangle, we will use the adhering to formula:

*

where a is the size of any kind of side of the triangle. Because an equilateral triangle has 3 equal sides, we deserve to use any side in the formula. To uncover the length of one side of the triangle, we will solve for a.

Now, we understand the perimeter that the it is intended triangle is 18in. So, we will substitute.

*

*

*

*

Therefore, the length of one side of the it is intended triangle is 6in.


Explanation:

An equilateral triangle has 3 same sides. So, to find the size of one side, we will use what us know. We understand the perimeter that the it is provided triangle is 39in. So, we will certainly look at the formula because that perimeter. Us get

*

where a is the length of one next of the triangle. So, to discover the length of one side, us will settle for a. Now, as proclaimed before, we know the perimeter that the triangle is 39in. So, we will substitute and solve because that a. We get

*

 

*

 

*

 

*

Therefore, the size of one next of the equilateral triangle is 13in.


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Example inquiry #5 : Equilateral triangles


The length of one next of an it is provided triangle is 6 inches. Provide the area the the triangle.


Possible Answers:
Correct answer:

*


Explanation:

*
,

where

*
 and 
*
room the lengths of two sides that the triangle and also
*
is the angle measure.

In an equilateral triangle, all of the sides have the very same length, and also all three angles are constantly

*
.

*

*


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Example question #6 : Equilateral triangles


The perimeter that an it is provided triangle is 

*
. Offer its area.


Possible Answers:
Correct answer:

*


Explanation:

An equilateral triangle v perimeter 

*
 has 3 congruent political parties of length

*

The area the this triangle is 

*

*
, so

*


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Example concern #7 : Equilateral triangles


The perimeter that an it is provided triangle is

*
. Offer its area.


Possible Answers:

The exactly answer is not among the other 4 choices.


Correct answer:

*


Explanation:

An it is provided triangle v perimeter

*
 has 3 congruent political parties of length

*

The area the this triangle is 

*


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Example question #8 : Equilateral triangles


The perimeter of an it is intended triangle is 

*
. Offer its area in terms of 
*
.


Possible Answers:
Correct answer:

*


Explanation:

An it is intended triangle through perimeter 

*
 has three congruent sides of length 
*
. Substitute this for 
*
 in the adhering to area formula:

*

*

*

*


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Example question #9 : Equilateral triangle


An equilateral triangle is inscribed within a one of radius 8. Offer its area.


Possible Answers:
Correct answer:

*


Explanation:

The cheat is to recognize that the circumscribed circle, or the circumcircle, has as its facility the intersection the the 3 altitudes that the triangle, and that this center, or circumcenter, divides every altitude right into two segments, one twice the size of the other - the longer one gift a radius. Due to the fact that of this, we have the right to construct the following:

*

We will uncover the area of 

*
, and also multiply the by 6.

*
, therefore the area of 
*
 is

*
.

Six time this - 

*
 - is the area of 
*
.


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Example concern #10 : Equilateral triangle


The perimeter the an it is intended triangle is

*
. Provide its area.

See more: How Many Oz To A Pint - What Is Weight Of A Pint Of Blueberries


Possible Answers:
Correct answer:

*


Explanation:

An it is intended triangle with perimeter 36 has three congruent sides of length

*

The area that this triangle is 

*


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