Find area of triangle ABC

Question

BD Perpendicular AC , AB =BC=a

Find the area of triangle ABC

I have tried Googling , I used formula 1/2 (base X Height) . Used Pythagorean theorem. Anyone can suggest me solution.

Answer 1

Let $y$ represent the distance $CD$. Then $y^2+x^2=a^2$, or $y=\sqrt{a^2-x^2}$. Now you have enough to find the area of triangle $BCD$ using your area formula. Double this to find the area of the whole triangle.

Answer 2

With reference to comments: Let's be supportive.

If BD is a perpendicular, then you can split ABC into two right-angled triangles, so it is easier to work with:

Then you can use the formula $Area = \frac{1}{2}\cdot base \cdot height$ for each triangle, and add the two. You'll need to find the size of the base of each triangle using the pythagorean theorem.