Answer
The error occurs in the calculationof the Height of the triangle.
The Height calculated is incorrect, the distance should be from y-coordinate 1 to y-coordinate 3.
Explanation
We want to find the error made in calculating the area of the triangle whose vertices are given by the coordinates A(4, 3), B(5, 1) and C(1, 1).
Note that
Area of a triangle = ½ × B × H
where
B = Base of the triangle
H = Perpendicular height of the triangle (that is the very straight vertical height of the triangle)
For the given triangle,
Base of the triangle lies between vertices C and B with coordinates (1, 1) and (5, 1) respectively.
We can easily see that B and C are on the same horizontal line (same y-coordinates), hence, the base of the triangle is simply the difference between the x-coordinates of B and C.
So,
Base = B = 5 -1 = 4
This is correct, no error there.
But, the perpendicular height of the triangle was calculated as the distance between vertices A and B.
This isn't a straight vertical line that makes a right angle with the horizontal. What was calculated as the perpendicular height is simply the length of a side of the triangle.
The triangle exists between y-coordinates 1 and 3, hence, the height of the triangle is where the error is.
The true height of the triangle = 3 - 1 = 2 units
The correct area of the triangle is
Area = ½ × B × H
= ½ × 4 × 2
= 4 square units.
Hope this Helps!!!