question_answer

The area of a triangle whose vertices are (-4, 0), (2, 4) and (4, 0) is

A)  8                            

B)         12

C)  16                           

D)         32            

Correct Answer: C

Solution :

 Draw a triangle with given vertices. As we know that area of the triangle is given by \[A=\frac{1}{2}\] (Base) (Height) So, we have to find the base and height of a triangle. Base,   \[b=4-(-4)=8\] For finding height, drop a perpendicular from \[(2,4)\] on to the base of a triangle as shown below                 Height, \[h=\sqrt{{{(2-2)}^{2}}+{{(4-0)}^{2}}}\]                 \[=\sqrt{16}=4\]               \[\therefore \] Area of given triangle \[=\frac{1}{2}\times b\times h\]                 \[=\frac{1}{2}\times 8\times 4=16\]