## King 3 years ago Help.......... L,M and N are midpoints on sides AB,BC,CA respectively.Area of triangle ABC is 48 units,then find area of triangle LMN......

1. k1r4

area of triangle LMN = $1/2*(64\sqrt{3}/4)*\sqrt{3}/2 = 12$

2. King

3. k1r4

4. King

yeah but i want the explanation as i already know the answer......

5. HerbvanH

The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

6. King

yeah i know that but wat do i do ahead?..

7. HerbvanH

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8. HerbvanH

Since they're all midpointsegments, they're all half the length of the opposing side. What would that do to your area?

9. HerbvanH

Original area is 1/2*A*B Area of small triangle is 1/2* 1/2A * 1/2B and that is 1/4 of the original area, get it?

10. King

oh ohk thanx.......

11. sheg

this triangle is divided into 4 equal parts so area of original triangle divided by 4