Use the sine rule to work out one of the sides. (a/sina = b/sinb = c/sinc) Then as it is an isosceles triangle the perpendicular dropped from the apex will (a) bisect the base and (b) form a right angle with the base. Now you know one side and the hypotenuse of a right-angled triangle and you use Pythagoras (a2 + b2 = c2) to solve the 'other' side of that, which is the height of the isosceles triangle.
Lets work it out:- If the legs are 12 and 16 inches, then a rectangle of that size would be 192 square inches in area. As the the diagonal of the rectangle makes two equal triangles (of legs 12 and 16 inches), the area of one of these is half the area of the triangle - 192/2 = 96 square inches.
In any triangle - not just right angled ones - the following holds true.* If angle A is opposite side a * and angle B is opposite side b * and angle C is opposite side cthen* SinAº/a = SinBº/b = SinCº/c (this is known as The Sine Rule)and* a2 = b2 + c2 − 2bc cosA (This is known as The Cosine Rule)So, all you ever need to know is three of the triangle's six properties and you can work out any of the others.
If you want to figure out just the area of the triangle, the formula is base times height divided by 2. It does not matter if it is inside a square, as long as you have the legnths of all they sides you need to calculate the area of that triangle. If you do not, It would be very difficult.
The side you use as the base does not matter. What does matter is that the height is the perpendicular distance between this side and the other vertex. If there is a right angle in the triangle, then use the two sides next to it as the base and height. Otherwise a bit of trigonometry will be required to work out the height of the triangle if it is not given.
It depends on what else you know about the triangle.
Knowing just the length of the base you can not work out the area. You need the height and the base or the length of the hypotenuse in order to work out the area.
Pythagoras theorem will always work with a right-angled triangle.
Add up the sides.
Measure it or check that it complies with Pythagoras' theorem.
I think you need at least one other piece of information. A length of a side? An angle? Is it a right angled triangle?
Sketch a net of the prism and and work out the area of each individual piece and then add them together
0.5 x side a x side b where a and b are any side except the longest one (the hypotenuse)
-- Measure or calculate the length of each of its 3 sides. -- Add the lengths of its 3 sides. -- The sum is the perimeter of the triangle.
A right triangle is easy, simply multiply the two sides and divide by two. A non-right triangle is a bit more of a challenge. You have to make it a right triangle by adding a right triangle to it. Calculate and then subtract the area of what you had to add.
The perimeter of a triangle is side A plus side B plus side C. Since we are talking about a right triangle, if you know two sides, then you know the third by the Pythagorean Theorem: A2 + B2 = C2
Use the cosine rule: a2 = b2+c2 - 2bc*cos A An isosceles triangle has two equal sides.