Answer:
169.7 cm²
Step-by-step explanation:
The ratios of side lengths in the special triangle with angles 30°-60°-90° are ...
1 : √3 : 2
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The given side is the shortest. The middle-length side is perpendicular to that, so is useful for figuring the area. Its length is √3 times the shorter side, so is LN=14√3 cm.
The area is given by ...
A = 1/2bh
A = 1/2(14 cm)(14√3 cm) = 98√3 cm²
A ≈ 169.7 cm²
The area of triangle LMN is about 169.7 cm².
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Additional comment
The other "special triangle" we work with is the 45°-45°-90° isosceles right triangle. Its side lengths have the ratios ...
1 : 1 : √2
