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# How do you get the area of a triangle without a base?

Updated: 12/18/2022

Wiki User

13y ago

it depends on the numbers you do get and what type of triangle it is. If somehow you can get it to be a right triangle and you have either the height or the hypotenuse, use the Pythagorean Theorem, A^2 +B^2=C^2... A and B being either the height or base and C being the hypotenuse. (side opposite the right angle is the hypotenuse)

The base side of a triangle can be any side of the triangle - the height of the triangle is the perpendicular distance from this side to the opposite vertex.

If you do not know the base length, then you must not know the length of any side of the triangle. You need to know one height and two other facts:

If you know all three heights of the triangle, then the area can be worked out using:

area = 1 ÷ (4 x √(h(h - 1/x)(h - 1/y)(h - 1/z)))

where

• x, y, and z are the three heights of the triangle; and
• h = 1/2 (1/x + 1/y + 1/z)

If you know the one height of the triangle and the angles at the ends of the base of the triangle, the base length can be worked out by trigonometry to give the area as:

area = 1/2(cot A + cot B)h2

where

• h is the height of the triangle; and
• A and B are the angles at the ends of the base.

Wiki User

13y ago