ISEE upper Level Math aid » Geometry » plane Geometry » triangle » Equilateral triangle

For an equilateral triangle, next A measures

and side B measures
. What is the length of next A?

Explanation:

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

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This means you can set the 2 values because that Side A and also Side B equal to one another, due to the fact that they measure up the exact same length, to resolve for

.

You now understand that

, but this is not your answer. The question asked for the length of side A, for this reason you must plug 3 right into that equation.

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

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

Explanation:

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

Explanation:

To discover the perimeter that an equilateral triangle, we will use the adhering to formula:

where a is the length of any kind of side the the triangle. Because an equilateral triangle has actually 3 same sides, we can use any kind of side in the formula. To find the size of one side of the triangle, we will deal with for a.

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

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

Explanation:

An equilateral triangle has 3 equal sides. So, to find the size of one side, us will use what we know. We recognize the perimeter that the equilateral triangle is 39in. So, we will certainly look in ~ the formula because that perimeter. We get

where a is the size of one next of the triangle. So, to discover the length of one side, us will resolve for a. Now, as proclaimed before, we know the perimeter the the triangle is 39in. So, we will certainly substitute and solve for a. Us get

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

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### Example inquiry #5 : Equilateral triangle

The size of one side of an it is provided triangle is 6 inches. Provide the area of the triangle.

Explanation:

,

where

and
are the lengths of 2 sides that the triangle and also
is the angle measure.

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

.

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### Example concern #6 : Equilateral triangle

The perimeter the an equilateral triangle is

. Provide its area.

Explanation:

An equilateral triangle through perimeter

has 3 congruent political parties of length

The area of this triangle is

, so

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### Example concern #7 : Equilateral triangle

The perimeter of an equilateral triangle is

. Give its area.

The correct answer is not among the other 4 choices.

Explanation:

An it is provided triangle v perimeter

has three congruent political parties of length

The area the this triangle is

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### Example concern #8 : Equilateral triangles

The perimeter the an it is provided triangle is

. Provide its area in state of
.

Explanation:

An it is intended triangle with perimeter

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

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### Example inquiry #9 : Equilateral triangles

An equilateral triangle is inscribed inside a circle of radius 8. Offer its area.

Explanation:

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

We will discover the area of

, and also multiply it by 6.

, so the area of
is

.

Six times this -

- is the area of
.

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### Example inquiry #10 : Equilateral triangle

The perimeter that an equilateral triangle is

. Provide its area.

Explanation:

An it is provided triangle v perimeter 36 has three congruent sides of length

The area the this triangle is

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