How to find the area of an equilateral triangle?

A triangle with all sides equal in length is called an equilateral triangle. All angles in an equilateral triangle are equal as well, each measuring 60 degrees. Read this post to find the area of an equilateral triangle.

How to find the area of an equilateral triangle?

The area of an equilateral triangle can be found using the formula A= 1/2 * b * h where b is the length of the base and h is the height of the triangle.

To find the height of the triangle, you can use the fact that the sides of an equilateral triangle are all equal. This means that the height is also equal to the length of the side.

Therefore, the formula for the area of an equilateral triangle can be simplified to A= 1/2 * b * b.

plug in the length of the base into the formula to find the area.

For example, if the length of the base is 10 cm, the area of the triangle would be 1/2 * 10 * 10 = 50 cm.

Area of an Equilateral Triangle – Formula, Derivation, Examples

The area of an equilateral triangle formula is given by the formula,

A = (1/4)*sqrt(3)*a*a

Where A = Area of the triangle and a = Length of the side of the triangle.

Proof of the formula:

Let a be the length of the side of an equilateral triangle.

Draw the perpendicular bisector of the side AB and produce it to C as shown in the figure below.

Join AC and BC.

Thus, triangle ABC is an equilateral triangle.

In triangle ABC,

AC = BC

AB = AB

∴ In triangle ABC,

ABC = BAC

∴ AB = AC

AC = AB

∠ACB = ∠ABC

∴ ∠ACB = ∠BAC

Therefore, ∠ACB = ∠ABC = ∠BAC

∴ ∠BAC = 60°

AB = BC

∴ AB = AC

What is the formula of an equilateral triangle?

A = (1/4) * √3 * a^2

A = (1/4) * √3 * s^2

Where:

A = Area of an equilateral triangle

a = Side of an equilateral triangle

s = Length of the side

√3 = Square root of 3

s = a * √3

A = (1/4) * 3 * a^2

A = (3/4) * a^2

And, A = (3/4) * s^2

How do you find the area of a equilateral triangle with just the height?

To find the area of a triangle with just the height, you need to know the length of the base. To find the length of the base, you can use the formula, base = 2 * height * tan(60).

So, the area of the triangle would be:

area = (1/2) * base * height
(1/2) * (2 * height * tan(60)) * height
height^2 * tan(60)
height^2 * 1.732

How do you find the area of an equilateral triangle without the height?

You can find the area of an equilateral triangle without the height by using the formula A=1/2bh, where b is the length of the base and h is the height.

To find the value of h, use the Pythagorean theorem. h^2=b^2-c^2, where c is the length of the side of the triangle.

Therefore, the area of the triangle is A=1/2bh=1/2b(b^2-c^2)=1/2b^2-1/2c^2.

You can use this formula to find the area of an equilateral triangle if you know the length of the base and the length of one side.

Conclusion

I hope this post will help you. If you have any questions, ask us. We are here to help you.

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