Question

tell me about the sum place ​

Answer 1

Given :-

• Diagonals of a trapezium ABCD with AB || CD, intersect each other at point 'O' .
• AB = 2CD .
• ∆AOB area = 96 cm².

To Find :-

• Area of ∆DOC = ?

Solution :-

from image we have,

→ ABCD is a trapezium .

→ AB ∣∣ DC .

now, in ∆AOB and ∆COD , we have,

→ ∠ABO = ∠CDO (Alternate angles.)

→ ∠BAO = ∠DCO (Alternate angles.)

→ ∠AOB = ∠COD (Vertically opposite angles.)

so,

→ ∆AOB ~ ∆COD (By AAA Similarity.)

now, we know that,

• If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

then,

→ Ar.∆AOB : Ar.∆COD = AB² : CD²

→ ∆AOB / ∆COD = (AB/CD)²

given that, AB = 2CD

→ 96 / Ar.∆COD = (2CD/CD)²

→ 96 / Ar.∆COD = (2/1)²

→ 96 / Ar.∆COD = 4 / 1

→ Ar.∆COD = 24 cm². (Ans.)

Hence, Area of ∆DOC will be 24 cm².

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

https://brainly.in/question/16655884