$In the diagram |LN| = 4cm, LNM = 90o and tan y = $\frac{2}{3}$. What is the area of the $\bigtriangleup$LMN?$

In the diagram |LN| = 4cm, LNM = 90^o and tan y = $\frac{2}{3}$ . What is the area of the $\bigtriangleup$ LMN?

24cm²

12cm²

10cm²

6cm²

Correct answer is B

Since tan y = $\frac{2}{3}$ and LN = 4

tan y = $\frac{2 \times 4}{3 \times 4} = \frac{8}{12} = \frac{4}{6}$

then tan y = $\frac{opp}{adj}$

MN = 6cm

Area of angle LMN = $\frac{1}{2}$ bh

= $\frac{1}{2} \times 6 \times 4$

= 12cm³

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