What is the area of scalene and equilateral triangles?

Answer 1

area of any triangle = ½base * height

But Hero's formula is useful, if you know the sides (a, b and c) but not the height

A = √[s(s - a)(s - b)( s - c)]
where s = ½ (a + b + c) (= semi-perimeter)

For an equilateral triangle A = ½ (bh)

But h = √3 * b/2

So A = √3 b² /4 where b = length of side

Note ... for an equilateral triangle hero's formula is as follows ... a = b = c and s = 3b/2

So s - a = s - b = s - c = 3b/2 - b = b/2

So A = √[s(s - a)(s - b)( s - c)]

= √[3b/2* b/2 * b/2 * b/2]

= √[3b^4 / 16]

= √3 b² /4 (same as above)

Answer 2

Sure they can. Isosceles, Scalene and Equilateral refer to the relationship between the lengths of the sides in a triangle. Just because the sides are different lengths doesn't mean that they can't share the same area.

Answer 3

Area of scalene triangle is √[s(s - a)(s - b)(s - c)]
where s = a+b+c/2
Area of equilateral triangle is √3/4 a^2...

Answer 4

by Heron's formula, if a, b, and c are the lengths of the three sides of a triangle, then the semi-perimeter
s = (1/2)(a + b + c), and the area
A = √[s(s - a)(s - b)(s - c)]

An equilateral triangle has an area of (s^2√3)/4, where s = the length of one side.

Answer 5

Area of a triangle: A = (1/2)b*h, where b denotes the base & h denotes the height, height is the length of a perpendicular line from the vertex, opposite the base, to a point on the base.

Answer 6

(base x height) /2

just remember height isnt the measure of any side except for in a right triange... it is the measure from the vertex that is not connected with the base line to the point where a line would meet perpendicularly with the base