The area of the triangle whose vertices are $(-2, a)(2,-6)$ and $(5,4)$ is 35 sq units then the value of '$\mathrm{a}$' is

The area of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is given by the formula:

Area = $\dfrac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

Substituting the given vertices $(-2, a)$, $(2, -6)$, and $(5, 4)$ and the area 35:

35 = $\dfrac{1}{2} |-2(-6 - 4) + 2(4 - a) + 5(a - (-6))|$

70 = $|-2(-10) + 8 - 2a + 5a + 30|$

70 = $|20 + 8 + 30 + 3a|$

70 = $|58 + 3a|$

This leads to two possible cases:

Case 1: $58 + 3a = 70$
$3a = 12$
$a = 4$

Case 2: $58 + 3a = -70$
$3a = -128$
$a = -\dfrac{128}{3}$

Comparing the results with the given options, $a = 4$ is present.

Answer: 4