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

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8.7

No. 1/2 base squared + height squared=side squared on an equilateral triangle.

An equilateral triangle with a height of 20 has a base of 23.1 (23.09401), not 15. If the base is 15 then the height will be 13 (12.99038).

2

Area = 1443.376 cm2

It is the height of the perpendicular line from its vertex to its base

The area of a triangle is one-half the product of the triangle's base and height. The height of an equilateral triangle is the distance from one vertex along the perpendicular bisector line of the opposite side. This line divides the equilateral triangle into two right triangles, each with a hypotenuse of 9c and a base of (9/2)c. From the Pythagorean theorem, the height must be the square root of {(9c)2 - [(9/2)c]}, and this height is the same as that of the equilateral triangle.

Height of an equilateral triangle = √3/2 x side = √3/2 x 20 = 10√3 ≈ 17.32

Height of an equilateral triangle = âˆš3 / 2 x side = (âˆš3 / 2 ) x 3 = 2.598 cm.

Cutting the equilateral triangle in half results in two right triangles each with a base of length x/2, and angles of 30, 60, and 90 degrees. Using the lengths of sides of a 30-60-90 triangle it can be found that the height is (x/2)√(3), which is the same as the height of the equilateral triangle.So the height of the equilateral triangle is x√(3) / 2.

By using Pythagoras' theorem

By using Pythagoras' theorem.

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