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.
1 answer:
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
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