Question

M is the midpoint of the side AB of a parallelogram ABCD. If ar (AMCD) = 24 cm², find ar (△ ABC).

Answer 1

Join the diagonal AC

From the figure we know that the diagonal AC divides the parallelogram ABCD into two triangles having the same area

It can be written as

Area of △ ADC = Area of △ ABC ……. (1)

We know that △ ADC and parallelogram ABCD are on the same base CD and between the same parallel lines DC and AM.

It can be written as

Area of △ ADC = Area of △ ABC = ½ (Area of parallelogram ABCD)

From the figure we know that M is the midpoint of AB

So we get

Area of △ AMC = Area of △ BMC = ½ (Area of △ ABC) = ½ (Area of △ ADC)

It can be written as

Area of AMCD = Area of △ ADC + Area of △ AMC

By substituting the values

24 = Area of △ ADC + ½ (Area of △ ADC)

It can be written as

24 = 3/2 (Area of △ ADC)

By cross multiplication

24 × 2 = 3 × (Area of △ ADC)

On further calculation

48 = 3 × (Area of △ ADC)

So we get

Area of △ ADC = 48/3

By division

Area of △ ADC = 16 cm²

From equation (1)

Area of △ ADC = Area of △ ABC = 16 cm²

Therefore, Area of △ ABC = 16 cm².