Question

In △ABC, point M is the midpoint of AC , point D is the midpoint of BC , and Area of triangle BMD=6 ft^2 . Find Area of triangle CMB and Area Of triangle ABC.

Answer 1

Answer    

Find out the Area of triangle ΔCMB and Area Of triangle ΔABC.

To proof

As given

In △ABC, point M is the midpoint of AC , point D is the midpoint of BC

Area of triangle ΔBMD=6 ft²

Now by using the property

The  median of a triangle divides the triangle into two triangles with equal areas.

As M and D is the midpoint

by using the property

Area of triangle ΔBMD = Area of triangle ΔCMD = 6 ft²

Total area of ΔCMB = Area of triangle ΔBMD + Area of triangle ΔCMD

                                  =  6 ft²  + 6 ft²

                                  = 12 ft²

area of ΔCMB = area of  ΔAMB= 12 ft²

( By using the property mentioned above )

Total area of ΔABC = area of ΔCMB+ area of  ΔAMB

                                = 12 + 12

                                 = 24 ft ²

Therefore the area of ΔABC is 24 ft ² and area of ΔCMB is 12ft²

Hence proved