Question

what is the area of triangle abc? 7 square units 15 square units 11 square units 3 square units

Explanation:

Step1: Calculate the area of the rectangle

The rectangle formed by \(x = 1,x = 4,y = 0,y = 5\) has length \(l=4 - 1=3\) and width \(w = 5\). Area of rectangle \(A_{r}=3\times5 = 15\) square units.

Step2: Calculate the area of the two right - angled triangles

• For the triangle with vertices \(A(1,1)\), \(B(4,0)\) and \((4,1)\): base \(b_1=4 - 1 = 3\), height \(h_1=1\). Area \(A_{1}=\frac{1}{2}\times3\times1=\frac{3}{2}\) square units.
• For the triangle with vertices \(B(4,0)\), \(C(3,5)\) and \((4,5)\): base \(b_2=4 - 3 = 1\), height \(h_2=5\). Area \(A_{2}=\frac{1}{2}\times1\times5=\frac{5}{2}\) square units.
• For the triangle with vertices \(A(1,1)\), \(C(3,5)\) and \((1,5)\): base \(b_3=5 - 1 = 4\), height \(h_3=3 - 1 = 2\). Area \(A_{3}=\frac{1}{2}\times4\times2 = 4\) square units.

Step3: Calculate the area of \(\triangle ABC\)

Using the formula \(A = A_{r}-A_{1}-A_{2}-A_{3}\)

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Answer:

7 square units