Question

In quadrilateral ABCD, diagonals AC and BD meet at O. If ∆AOB, ∆DOC and ∆BOC have areas 3cm², 10cm² and 2cm² respectively, find the area of ∆AOD in cm²​

Answer 1

Area of ∆ AOD = 15 cm^2.

Step-by-step explanation:

In ∆s, AOB and BOC, height is common.

Area of ∆s AOB and BOC =

$\frac{1}{2} \times AO \times height \: \: and \\ \: \: \frac{1}{2} \times OC \times height$

Therefore, Ar. ∆ AOB : Ar. ∆ BOC = AO : OC

=> AO : OC = 3 : 2

{ 1/2 and height will get cancelled }

Similarly, Ar. ∆ AOD : Ar. ∆ DOC = AO : OC

But AO : OC = 3 : 2

=> Ar. ∆ AOD : 10 = 3 : 2

=> Ar. ∆ AOD = (10 × 3) ÷ 2 = 15 cm^2

Hence, area of ∆ AOD = 15 cm^2.