In the trapezoid abcd with bases ad and bc, the diagonals intersect at a point o

| January 31, 2021 | education

In the trapezoid abcd with bases ad and bc, the diagonals intersect at a point o, which is 4 cm away from the line cd.Find the area of the triangle aob if cd = 8 cm.

In the СOD triangle, the OH segment is its height, then the area of ​​the СOD triangle is equal to:

Sod = СD * OH / 2 = 8 * 4/2 = 16 cm2.

Consider the AВD and AСD triangles.

In the triangles AВD and AСD there is a common base of blood pressure.

Let’s build the height of the CК of the trapezoid, which is also the height of the AВD and AСD triangles, then:

Savd = AD * CК / 2.

Sasd = AD * СК / 2.

Savd = Sasd.

The AВD triangle consists of two triangles, AOB and AOD, the AВD triangle consists of СOD and AOD triangles.

Then Savd = Sаov + Sаod.

Sasd = Ssod + Sаod.

Saov + Saod = Scod + Saod.

Saov = Scod = 16 cm2.

Answer: The area of ​​the AOB triangle is 16 cm2.



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