High school Math help » Geometry » aircraft Geometry » triangles » Equilateral triangle » exactly how to uncover the area the an it is provided triangle

An it is intended triangle has a side length of

. What is the triangle"s area?

The area of square ABCD is 50% higher than the perimeter of the it is provided triangle EFG. If the area the square ABCD is equal to 45, climate what is the area the EFG?

Explanation:

If the area the ABCD is equal to 45, climate the perimeter of EFG is equal to x * 1.5 = 45. 45 / 1.5 = 30, for this reason the perimeter of EFG is same to 30. This method that each side is equal to 10.

You are watching: Express the area of an equilateral triangle as a function of the length of a side x.

We then use the formula for the area that a triangle, i beg your pardon is 1/2 * b * h. We acquire 1/2 * 10 * 5√3 = 5 * 5√3 = 25√3.

In general, the height of an equilateral triangle is same to √3 / 2 time a next of the equilateral triangle. The area that an it is provided triangle is equal to 1/2 * √3s/ 2 * s = √3s2/4.

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### Example inquiry #1 : just how To find The Area that An equilateral Triangle

What is the area the an equilateral triangle through sides 12 cm?

18√3

12√2

54√2

72√3

36√3

36√3

Explanation:

An equilateral triangle has actually three congruent sides and also results in three congruent angles. This figure results in 2 special best triangles ago to back: 30° – 60° – 90° providing sides of x - x √3 – 2x in general. The height of the triangle is the x √3 side. Therefore Atriangle = 1/2 bh = 1/2 * 12 * 6√3 = 36√3 cm2.

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### Example concern #4 : how To uncover The Area that An it is intended Triangle

The size of one side of an it is provided triangle is ten. What is the area the the triangle?

Explanation:

The size of the hypotenuse will be one side of the equilateral triangle.

.

The side of the it is provided triangle that represents the height of the triangle will have actually a size of

because it will be the opposite the 60o angle.

To calculate the area of the triangle, multiply the base (one side of the it is provided triangle) and the elevation (the perpendicular bisector) and also divide by two.

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### Example concern #5 : how To discover The Area of An it is provided Triangle

What is the area that an it is provided triangle through a side size of

?

Not enough information to solve

Explanation:

In order to discover the area of the triangle, us must very first calculate the height of its altitude. One altitude slices an it is provided triangle into two

triangles. This triangles monitor a side-length pattern. The smallest of the two legs equals
and the hypotenuse equals
. By way of the Pythagorean Theorem, the longest foot or
.

Therefore, we can uncover the elevation of the altitude that this triangle by designating a worth for

. The hypotenuse of one of the
is additionally the side of the initial equilateral triangle. Therefore, one can say that
and
.

Now, we deserve to calculate the area of the triangle via the formula

.

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### Example concern #6 : how To discover The Area the An it is intended Triangle

An equilateral triangle has a side size of

find its area.

Not enough information to solve

Explanation:

In order to uncover the area the the triangle, us must very first calculate the elevation of that is altitude. An altitude slices an equilateral triangle right into two

triangles. These triangles follow a side-length pattern. The the smallest of the 2 legs equals
and the hypotenuse equals
. By way of the Pythagorean Theorem, the longest foot or
.

Therefore, us can find the elevation of the altitude of this triangle through designating a value for

. The hypotenuse of among the
is likewise the side of the original equilateral triangle. Therefore, one can say

that

and
.

Now, we deserve to calculate the area the the triangle via the formula

Now convert to meters.

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### Example inquiry #7 : just how To find The Area the An equilateral Triangle

Triangle A: A appropriate triangle with sides size

,
, and
.

Triangle B: An it is intended triangle through side lengths

.

Which triangle has a better area?

The areas of the two triangles room the same.

There is not enough information offered to identify which triangle has a greater area.

Triangle B

Triangle A

Triangle B

Explanation:

The formula because that the area that a appropriate triangle is

, where
is the size of the triangle"s basic and
is the height. Since the longest side is the hypotenuse, use the two smaller numbers offered as sides because that the base and also height in the equation to calculation the area that Triangle A:

The formula because that the area of an equilateral triangle is

, where
is the size of every side. (Alternatively, you can divide the it is provided triangle into two right triangles and find the area of each). Triangle B"s area is thus calculated as:

To identify which of the two locations is higher without utilizing a calculator, rewrite the locations of the two triangles with similar factors. Triangle A"s area can be expressed as

, and Triangle B"s area have the right to be expressed as
. Since
is greater than
, the product that the determinants of Triangle B"s area will be greater than the product of the determinants of Triangle A"s, therefore Triangle B has actually the better area.

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### Example question #1 : how To discover The Area the An it is intended Triangle

What is the area the an equilateral triangle v side 11?

Explanation:

Since the area of a triangle is

.

Then, multiply that by the base (11).

Finally, divide it by 2 to acquire 52.4.

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### Example question #9 : just how To discover The Area the An it is intended Triangle

Find the area of the adhering to equilateral triangle:

Explanation:

The formula for the area that an equilateral triangle is:

Where

is the size of the side

Plugging in our values, we get:

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### Example concern #10 : just how To find The Area the An equilateral Triangle

Determine the area of the following equilateral triangle:

Explanation:

The formula for the area of an it is provided triangle is:

,

where

is the size of the sides.

Plugging in our value, we get:

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