Question

im confused about finding the area of a triangle how do you do it??? exactly step by step

Answer 1

(a * b)/2

Answer 2

What kind of triangle? No... just kidding. ANY triangle is the same. you need the length of one side and the length to the point 90 degrees from that side... so the 2 right angle sides of a right angle or the base and height of any other..
Then it's just half the product of the 2.

Answer 3

Are you talking about derivation of the formula alex?

Answer 4

yea

Answer 5

I think you need definite integrals for that, do you know definite integrals?

Answer 6

so if the question is 9.4, 15.7, 12.6 then the answer would be ? wait do i just need to multiply everything?

Answer 7

u use hero's formula for this

Answer 8

whats the formula for that one?

Answer 9

\[A = \sqrt { (s)(s-a)(s-b)(s-c)}\]

where a, ,b ,c are the 3 sides
and s = (a+b+c)/2

Answer 10

im in 5th grade i dont know exactly what that is.......... wait i have to add everything and divied it by 2?

Answer 11

yes

Answer 12

Typically at that level of mathematics you will be given the base and the height, and all you need to know is that the area is:

\[\frac{1}{2}\times Base \times Height\]

Answer 13

ok i think i can remember that

Answer 14

thank u

Answer 15

to me>??

Answer 16

You dont need indefinite integrals to derive the formula for the area of a triangle. Consider a rectangle of length a and height b as in attached diagram. The area of teh rectangle is the base a times its height b. or \[Area=ab\].

Now draw a diagonal line from one corner to the other, and yoi bisect the rectangle into two triangles of base a and height b. Since you have divided the rectangle by into two triangles, then each triangle must have half the area of the rectangle. hence the area of the triangle is \[A=\frac{1}{2}ab\], which holds true for any triangle.

Answer 17

"so if the question is 9.4, 15.7, 12.6 then the answer would be ?"

I'm a bit confused about what the op wants.

If the 3 figures above are the sides, it is one question.

Or is the op just asking a general question about triangle areas?

Answer 18

but jony those are only for right angled triangles!

Answer 19

That's OK, you can drop a perp from any point to the base and make 2 rights...

Answer 20

"so if the question is 9.4, 15.7, 12.6 then the answer would be ?"

In fact, these figures are very close to a right triangle.

Answer 21

Maybe the op was given base and altitude and chose to calculate the hypotenuse.

Answer 22

In which case the "answer" would be 1/2 * 9.4 * 12.6

Answer 23

Hi mashy,

The example is the simplest case appropriate to 5th grade level, to show where the formula comes from. As pointed out by estudier, it is still applicable for non-right angle triangles as long as you use the length perpendicular to a designated "base" to calculate the area. see attached diagram.

In this diagram we can draw lines (black lines) such that the rectangle of length a and height b, is split into 3 unequal triangles. Now we want to know the area of the largest triangle, which is not a right angle triangle. So lets draw another line from the top vertex to the base of the triangle so that this line is perpendicular to the base marked in red. Not only does this split the triangle in two unequal segments, but it will also split the rectangle into two rectangles now of length c and height b, and one of length d and height b. We can then apply the previous triangle proof, and show that the area of the triangle on the left is equal to \[A_{left}=\frac{1}{2}cb\] and that the triangle on teh left is \[A_{right}=\frac{1}{2}db\] the total area of the larger triangle is then the sum of these two is\[A=A_{left}+A_{right}=\frac{1}{2}b(c+d)\]. But clearly \[(c+d)=a\] therefore the total area of the desired triangle is \[A=\frac{1}{2}ab\].
This can be done for any type of triangle, which is why I pointed out it holds true for any triangle.