Question

What is the area formula of an obtuse triangle?

Answer 1

Hint: In order to solve the question given above, you need to recall the area of any triangle. You will notice that the area of all the triangles is the same. The formula for the area of a triangle is \[\dfrac{1}{2} \times base \times height\]. Keep this formula in mind while proving that the result is the same for an obtuse triangle.
Formula used:
To find out the area formula of an obtuse triangle, we need to know the area of any triangle.
Area of a triangle \[ = \dfrac{1}{2} \times base \times height\].

Complete step-by-step answer:
Before starting to solve the above question, you need to keep this in mind that the area of any triangle is equal to half of the product of its base by its altitude. This includes the obtuse triangles also.
Now, to better understand this question let us first draw a triangle.

Now, the area of this triangle equals the difference between the area of \[\vartriangle ABD\] and \[\vartriangle ACD\].
So, area of \[\vartriangle ABD\] equals to:
\[{S_{ABD}} = \dfrac{1}{2} \times BD \times h\].
And the area of \[\vartriangle ACD\] equals to
\[{S_{ACD}} = \dfrac{1}{2} \times CD \times h\] .
The difference of both the areas is equal to
\[{S_{ABC}} = \dfrac{1}{2} \times BD \times h - \dfrac{1}{2} \times CD \times h\]
  \[
   = \dfrac{1}{2}\left( {BD - CD} \right)h \\
   = \dfrac{1}{2} \times a \times h \;
 \]
So, the formula for an obtuse triangle is \[\dfrac{1}{2} \times a \times h\]. This is the same as for any other triangle with all acute angles.
So, the correct answer is “\[\dfrac{1}{2} \times a \times h\]”.

Note: While solving questions similar to the one given above, one very important point that you need to always keep in your mind is that the area of any triangle is equal to half of the product of its base by its altitude. So, we can say even for an obtuse triangle the formula for calculating the area is \[\dfrac{1}{2} \times base \times height\].