Question

in the square ABCD, and E is the mid point of CD, BD and AE intersect at point O if the area of triangle AOB is 36m2 then what will be the area (in m2) of triangle ODE​

Answer 1

Answer:

your questions is not clear

Answer 2

Given: in the square ABCD, and E is the mid point of CD, BD and AE intersect at point O if the area of triangle AOB is 36m2

To find: The area (in m2) of triangle ODE​.

Solution:

The angles AOB and DOE are vertically opposite angles and hence, they are equal. The angles OAB and OED are interior alternate angles and hence, are equal. The angles OBA and ODE are also interior alternate angles and hence, are equal. So, the triangles AOB and DOE are similar to each other by AAA (angle-angle-angle) theorem.

Since E is the midpoint of CD, AB is twice the length of DE. Now, these two sides can be written in proportion with the areas of the two triangles as follows.

$(\frac{AB}{DE})^{2} = \frac{Ar.ABO}{Ar.ODE}$

$AB = 2DE$

$(\frac{2DE}{DE})^{2} = \frac{36}{Ar.ODE}$

$Ar.ODE = \frac{36}{4}$

               $= 9 m^{2}$

Therefore, the area (in m2) of triangle ODE​ is 9 m².