Question

ABCD is a parallelogram p and q are the midpoints of sides ab and CD respectively show that area of triangle A P Q equal to 1 by 8 of area of parallelogram ABCD​

Answer 1

le lag the midpoint of side ab and CD be p q

as we that this t this is a theorem that tell us when we join the midpoint of two opposite sides the area of the parallelogram equals to twice the area of smaller

so area of parallelogram a p q d equals to half of parallelogram ABCD ..(1)

the another germs that when a triangle and a parallelogram on the same base and between same parallel lines then the area of triangle is twice the area of parallelogram so

area of parallelogramAPQD =HALF AREA OF TRIANGLE APQ

from first equation we get that

area of triangle a p q equals to 1 by 4 of parallelogram ABCD

hence proved