Question

error analysis describe and correct the error in finding the area
x
b(5, 1)
4
a(4, 3)
2
2 4 6 x
-2
c(1, 1)
b = |5 - 1| = 4
h = √((5 - 4)²+(1 - 3)²)
= √5
≈ 2.2
a = 1/2bh ≈ 1/2(4)(2.2)=4.4
the area is about 4.4 square units.

Explanation:

Step1: Identify the error in base - height concept

The error is using the distance between non - parallel points as height. For a triangle, the height must be perpendicular to the base. Here, the base is the horizontal distance between \(x = 1\) and \(x = 5\), but the calculated height is the distance between \(A(4,3)\) and \(B(5,1)\) which is not perpendicular to the base.

Step2: Correctly find the base and height

The base \(b\) is the horizontal distance between \(C(1,1)\) and \(B(5,1)\), so \(b=|5 - 1|=4\). The height \(h\) is the vertical distance from \(A(4,3)\) to the line \(y = 1\), so \(h=|3 - 1| = 2\).

Step3: Calculate the area

Using the formula \(A=\frac{1}{2}bh\), we substitute \(b = 4\) and \(h=2\). Then \(A=\frac{1}{2}(4)(2)=4\).

Answer:

The correct area is 4 square units.