Question

What is the area of a triangle whose vertices are (a, b + c), (a, b - c) and (-a, c)?

• A. |2ab|
• B. |4ac|
• C. |2ac|
• D. Triangle can't be formed

Answer 1

The correct option is C

|2ac|

Area of the triangle = $\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$
$\frac{1}{2}\left[a\right(b-c-c]+a(c-b-c)-a(b+c-b+c\left)\right]$
$\frac{1}{2}\left[a\right(b-2c)+a(-b)-a(2c\left)\right]=-2ac$
The area of a triangle can never be a negative quantity, so we always take the modulus of the value
So, the area is |-2ac| =|2ac|