Question

the coordinate plane shows triangle abc. what is the area of the triangle? enter your answer in the box. square units

Explanation:

Step1: Find the area of the rectangle

Assume the rectangle that encloses the triangle has length \(6\) (from \(x = 2\) to \(x=8\)) and height \(5\) (from \(y = 1\) to \(y = 6\)). The area of the rectangle \(A_{rectangle}=l\times w=(8 - 2)\times(6 - 1)=6\times5 = 30\).

Step2: Subtract the areas of the three right - angled triangles

• Triangle 1: Base \(b_1=(6 - 2)=4\), height \(h_1=(4 - 1)=3\). Area \(A_1=\frac{1}{2}\times4\times3 = 6\).
• Triangle 2: Base \(b_2=(8 - 6)=2\), height \(h_2=(6 - 1)=5\). Area \(A_2=\frac{1}{2}\times2\times5=5\).
• Triangle 3: Base \(b_3=(8 - 2)=6\), height \(h_3=(6 - 4)=2\). Area \(A_3=\frac{1}{2}\times6\times2 = 6\).

The area of \(\triangle ABC\) is \(A = 30-(6 + 5+6)=13\).

Answer:

\(13\)