ABCD is a trapezium in which AB is parallel to CD, AB = 12 cm and CD = 24 cm. If O is the point of intersection of AC and BD, find the ratio of the area of triangle AOD to that of triangle COD.

Question

Answer 1

Let the height of the trapezium be h. Triangles AOB and COD are similar. AB/CD = 1/2. So, height of triangle AOB / height of triangle COD = 1/2
So, height of triangle AOB = h/3 and height of triangle COD = 2h/3.

Area of triangle ADC = 1/2 * 24 * h
Area of triangle COD = 1/2 * 24 * 2h/3
Area of triangle AOD = Area of triangle ADC - Area of triangle COD = 1/2 * 24 * (h - 2h/3) = 1/2 * 24 * h/3

So, required ratio = 1/2 * 24 * h/3 / 1/2 * 24 * 2h/3 = 1/2

Answer 2

Let the height of the trapezium be h. Triangles AOB and COD are similar. AB/CD = 1/2. So, height of triangle AOB / height of triangle COD = 1/2
So, height of triangle AOB = h/3 and height of triangle COD = 2h/3.

Area of triangle ADC = 1/2 * 24 * h
Area of triangle COD = 1/2 * 24 * 2h/3
Area of triangle AOD = Area of triangle ADC - Area of triangle COD = 1/2 * 24 * (h - 2h/3) = 1/2 * 24 * h/3

So, required ratio = 1/2 * 24 * h/3 / 1/2 * 24 * 2h/3 = 1/2

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ABCD is a trapezium in which AB is parallel to CD, AB = 12 cm and CD = 24 cm. If O is the point of intersection of AC and BD, find the ratio of the area of triangle AOD to that of triangle COD.