ISEE top Level Math aid » Geometry » plane Geometry » triangle » Equilateral triangles

For an it is intended triangle, side A measures

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


Explanation:

First you must recognize the for an equilateral triangle, all 3 sides have actually equal lengths.

You are watching: How many degrees in an equilateral triangle

This means you can set the two values because that Side A and also Side B same to one another, since they measure up the same length, to deal with for 

*
.

*

*

*

*

You now know that 

*
, yet this is not your answer. The concern asked because that the size of side A, therefore you have to plug 3 into that equation.

*

*

*

So the size of next A (and next B for that matter) is 8.

 


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


Explanation:

An it is provided triangle is one in which all 3 sides space congruent. It likewise has the home that all three interior angles space equal. In other words, all three angles the an it is intended triangle are constantly 60°. Because all sides are congruent, the various other two sides both measure 12 centimeters.


*


*


*


*


Explanation:

To find the perimeter the an equilateral triangle, us will usage the adhering to formula:

*

where a is the length of any side of the triangle. Due to the fact that an it is intended triangle has actually 3 equal sides, we have the right to use any kind of side in the formula. To find the length of one side of the triangle, we will fix for a.

Now, we recognize the perimeter of the it is provided triangle is 18in. So, we will substitute.

*

*

*

*

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


Explanation:

An it is intended triangle has actually 3 equal sides. So, to uncover the size of one side, we will usage what us know. We recognize the perimeter the the it is provided triangle is 39in. So, we will look in ~ the formula because that perimeter. We get

*

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

*

 

*

 

*

 

*

Therefore, the length of one next of the it is provided triangle is 13in.


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Example concern #5 : Equilateral triangles


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


Possible Answers:
Correct answer:

*


Explanation:

*
,

where

*
 and 
*
space the lengths of two sides the the triangle and
*
is the angle measure.

In an it is intended triangle, all of the sides have actually the very same length, and all 3 angles are always

*
.

*

*


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Example question #6 : Equilateral triangle


The perimeter of an equilateral triangle is 

*
. Offer its area.


Possible Answers:
Correct answer:

*


Explanation:

An it is intended triangle through perimeter 

*
 has 3 congruent political parties of length

*

The area of this triangle is 

*

*
, so

*


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Example question #7 : Equilateral triangles


The perimeter of an equilateral triangle is

*
. Provide its area.


Possible Answers:

The exactly answer is not amongst the other 4 choices.


Correct answer:

*


Explanation:

An equilateral triangle through perimeter

*
 has three congruent political parties of length

*

The area that this triangle is 

*


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Example concern #8 : Equilateral triangles


The perimeter of an it is intended triangle is 

*
. Offer its area in state of 
*
.


Possible Answers:
Correct answer:

*


Explanation:

An it is intended triangle with perimeter 

*
 has 3 congruent political parties of length 
*
. Substitute this for 
*
 in the adhering to area formula:

*

*

*

*


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Example inquiry #9 : Equilateral triangle


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


Possible Answers:
Correct answer:

*


Explanation:

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

*

We will find the area of 

*
, and multiply it by 6.

*
, therefore the area of 
*
 is

*
.

Six times this - 

*
 - is the area of 
*
.


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Example inquiry #10 : Equilateral triangle


The perimeter of an it is provided triangle is

*
. Provide its area.

See more: Does Hennessy Have Pork In It ? Inside Hennessy


Possible Answers:
Correct answer:

*


Explanation:

An equilateral triangle with perimeter 36 has three congruent sides of length

*

The area the this triangle is 

*


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