Question

what is the area of triangle lmn?6 square units4 square units3 square units8 square units

Explanation:

Step1: Calculate the area of the rectangle

The rectangle formed by \(L\), \(P\), \(M\) and the extension has length \(2\) (from \(x = 1\) to \(x=2\)) and height \(4\) (from \(y=- 1\) to \(y = 3\)). Area of rectangle \(A_{rectangle}=2\times4 = 8\) square units.

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

• Triangle 1: With base \(2\) (from \(x = 1\) to \(x = 2\)) and height \(3\) (from \(y=-1\) to \(y = 2\)). Area \(A_{1}=\frac{1}{2}\times2\times3=3\) square units.
• Triangle 2: With base \(2\) (from \(x = 1\) to \(x = 2\)) and height \(1\) (from \(y = 2\) to \(y = 3\)). Area \(A_{2}=\frac{1}{2}\times2\times1 = 1\) square units.

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

Using the formula \(A = A_{rectangle}-A_{1}-A_{2}\). Substitute the values: \(A=8 - 3-1=4\) square units.

Answer:

4 square units