Question

in triangle ABC , O and E are midpoints of AB and AC , M and N are the midpoint of AO and AE find the ratio of area of triangle AMN and area of AOE : area of triangle ABC

Answer 1

Answer: $\frac{5}{16}$

Step-by-step explanation:

The line joins the mid point of one side and the opposite vertex  is called the median of the triangle.

And, A median divides a triangle into two equal parts.

Let the area of the triangle ABC = x square unit..

AO is the median of the triangle  ABC

⇒Area of triangle AOC = 1/2 × area of AB = x/2

OE is the median of triangle AOC

⇒ Area of triangle AOE = 1/2 × area of triangle AOC = 1/2 × x/2 = x/4 square unit.

AN is the median of triangle AOE

Area of Δ AON = 1/2 × Area of Δ AOE = x/8

MN is the median of triangle AON,

⇒ Area of Δ AMN = 1/2 × Area of AON = x/16

⇒ Area of triangle AMN + Area of AOE : Area of triangle ABC

⇒ x/16 + x/4 : x

⇒ 5x/16 : x

⇒ 5 : 16