Area of parallelogram

Question

In triangle ABC, B=90º and BC=16 cm . M and N are the mid-points of AB and AC respectively . If triangle ABC= 64 cm² , find the area of the quadrilateral MBCN.

Answer 1

Hi Sanjay,

 

Let's begin by drawing a diagram for this problem.  Below is our diagram for this problem:

 

https://dl.dropbox.com/s/q3g1tk7iui8lcds/Diagram_for_Solving_Area_of_Quadrilateral%20MBCN.png?raw=1

 

Next, we know that line MN joining the midpoints of sides AB and AC of triangle ABC is parallel and equal to 1/2 the third side (BC) via the Triangle Mid Segment theorem:

    MN = 1/2(16) = 8

 

Next, we know that altitude MB of quadrilateral MBCN is 1/2 of side AB of triangle ABC, since M is said to be the midpoint of side AB.  Therefore, if we can determine length of AB then we can determine length of MB:

     Area ABC = 64 (given)

     BC = 16 (given)

     (1/2)(16)(AB) = 64

     8(AB) = 64

     AB = 64/8

     AB = 8

     MB = 8/2

     MB = 4

 

Now we have everything we need to calculate the area of trapezoid MBCN:

    MB = 4 (calculated above)

    MN = 8 (calculated above)

    BC = 16 (given)

    Area MBCN = 1/2(4)(8 + 16)

    Area MBCN = 2(24)

    Area MBCN = 48

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.