# Thread: height of a traingle

1. ## height of a traingle

Hi, i have a question where as it tells me that i need to find the area, i know to find the area of a traingle its half the base times the height, just i don't have the height and don't know how to find it inorder to find the area. the triangle is isoceles and has a 8cm base two sides are 5cm each and it has a dashed line for the height (h) with the square thing 90c angle. please help me find the height

2. Originally Posted by blmg911
Hi, i have a question where as it tells me that i need to find the area, i know to find the area of a traingle its half the base times the height, just i don't have the height and don't know how to find it inorder to find the area. the triangle is isoceles and has a 8cm base two sides are 5cm each and it has a dashed line for the height (h) with the square thing 90c angle. please help me find the height
Using the Pythagorean theorem, where $\displaystyle a^2 + b^2 = c^2$ (and c is the hypotenuse)

First split this triangle in your mind into two triangles, where the halfway point cuts the isosceles triangle in half, we will have two 90 degree triangles.

Looking at the picture of one of these triangles, it should be clear that the hypotenuse is 5, and we'll choose a to be our height, and so b will be half of 8 (aka 4), note that it is 4 because it is isosceles, otherwise the halfway point may not be where the dotted line connects to the base.

so $\displaystyle a^2+4^2=5^2~~~~\Rightarrow~~~~a^2+16=25~~~~\Righta rrow~~~~a^2=9~~~~\Rightarrow~~~~a=\pm 3$

And because it is illogical to have a negative length, we choose the positive value of 3.

So our height is 3.

then 3*8/2=12 so the area is 12 units squared.

3. ## Thanks

Thanks but i just kept going till i found a simple way. which was one side (5) plus half the base =9 which i then worked out the square root which is 3 much easier but thanks.

4. Not only was Angel_White's answer the simple way, it was the right way!