Question

In the given figure ABCD is a parallelogram and M is the midpoint of AB, and N the midpoint of BC then find the area of shaded region if the area of the parallelogram is 75 cm²
a. 37.5
b. 25
c. 32.5
d. 20​

Answer 1

area of parallelogram subtracted by area of shaded area hope it can help please mark this brainalist

Answer 2

Answer:

Step-by-step explain

In this M and N are mid points so the area of triangle DCN and triangle ADM is 75/4 because the line joining mid points of the opposite side of parallelogram divide the area into two equal parts and their diagonal DM and similarly in case of triangle DCN the diagonal DN divide the half area of parallelogram to its half so the area is 75/4.

Now ,

See triangle AOM and DOC these are similar Triangle and the side ratio is 1:2

MO:DO= 1:2

So in triangle AMD with base DM area divided in ratio of 1:2

so area of triangle AOM is (75/4)*(1/3)=25/4  and area of triangle AOD is (75/4)*(2/3)=50/4.

Similarly in case of triangle DCN with base DN area divided in ratio of 1:2

so area of triangle NPC is (75/4)*(1/3)=25/4  and area of triangle DPC is (75/4)*(2/3)=50/4.

So in triangle ADC the area of ODP is (75/2)-(50/4)-(50/4)=25/2

Similarly in case of other half of parallelogram, triangle ABC

area of OPMBN is (75/2)-(25/4)-(25/4)=25

so the answer is triangle DOP+AOM+NCP is (25/2)+(25/4)+(25/4)= 25