# In the quadrangle ABCD, the areas are known: S1 of the triangle ABO = 10, S2 of the triangle BOC = 20, S3

October 7, 2021 | education

| **In the quadrangle ABCD, the areas are known: S1 of the triangle ABO = 10, S2 of the triangle BOC = 20, S3 of the triangle COD = 60. Find the area ABCD (i.e., the intersection point of the diagonals).**

Consider triangles ABO and BOC, the areas of which are 10 cm2 and 20 cm2, respectively.

The triangles ABO and BOC have a total height BH, then the ratio of the bases of the triangles is equal to the ratio of their bases. CO / AO = Svos / Savo = 20/10 = 2.

In the triangles SOD and AOD, the total height of the DC, then CO / AO = Scod / Saod.

2 = Sod / Saod.

Saod = Scod / 2 = 60/2 = 30 cm2.

Then Savsd = Saov + Svos + Sod + Saod = 10 + 20 + 60 + 30 = 120 cm2.

Answer: The area of the AVSD quadrangle is 120 cm2.

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