Question 79

What would be the area of a triangle formed by the medians of an equilateral triangle that has a side length of 12 cm?

The area of a triangle formed by the medians of an equilateral triangle would be (3/4) of the area of the original triangle. 

The area of the original equilateral triangle can be calculated using the formula $$\frac{\sqrt{\ 3}}{4}a^2$$, where $$a$$ is the side length, giving the area of the original equilateral triangle to be $$\frac{\sqrt{\ 3}}{4}\times\ 12\times\ 12$$

This would give the area of the triangle formed by the medians to be $$\frac{\sqrt{\ 3}}{4}\times\ 12\times\ 12\times\ \frac{3}{4}=27\sqrt{\ 3}cm^2$$

Therefore, Option C is the correct answer. 

Video Solution

video

Create a FREE account and get:

  • Download Maths Shortcuts PDF
  • Get 300+ previous papers with solutions PDF
  • 500+ Online Tests for Free