In both cases, the area of the triangle can be computed from the formula
A = (1/2)bh
where b is the length of the base, and h is the height perpendicular to the base.
1. It is convenient to use DE as the base. Its length is 4-1 = 3. Then the height is the distance from F to DE, which is 1-(-3) = 4. By the formula, the area is
A = (1/2)(3)(4) = 6
2. It is convenient to use LK for the base. Its length is 4-0 = 4. Then the height is the distance from J to the line y=-5, which is -1-(-5) = 4. By the formula, the area is
A = (1/2)(4)(4) = 8