
An it is intended triangle has a side length of





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?
Possible Answers:
18√3
12√2
54√2
72√3
36√3
Correct answer:
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?
Possible Answers:
Correct answer:

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


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

Possible Answers:
Not enough information to solve
Correct answer:

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




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







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

Possible Answers:
Not enough information to solve
Correct answer:

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




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


that




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



Triangle B: An it is intended triangle through side lengths

Which triangle has a better area?
Possible Answers:
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
Correct answer:
Triangle B
Explanation:
The formula because that the area that a appropriate triangle is





The formula because that the area of an equilateral triangle is





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




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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?
Possible Answers:
Correct answer:

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:

Possible Answers:
Correct answer:

Explanation:
The formula for the area that an equilateral triangle is:

Where

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:
Possible Answers:
Correct answer:

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

where

Plugging in our value, we get:

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