Understanding Q...

$$ABCD$$ is a parallelogram and $$P$$ is a point on the segment $$\overline {AD}$$ dividing it internally in the ratio $$3 : 1$$ the line $$\overline {BP}$$ meets the diagonal $$\overline {AC}$$ in $$Q$$. Then the ratio $$AQ:QC$$ is

$$ABCD$$ is a parallelogram $$X$$ and $$Y$$ are the mid points of $$BC$$ and $$CD$$ respectively. Then, ar(parallelogram $$ABCD$$) is

Let ABC is given triangle having respective sides a, b, c. D, E, F are points of the sides BC, CA, AB respectively so that AFDE is a parallelogram. The maximum area of the parallelogram is?

The perimeter of a parallelogram is $$38 \text{ cm}$$. If the longer side is $$11 \text{ cm}$$, find the length of shorter side.

How many unique measurements are needed to construct a parallelogram.

The point of intersection of the diagonals of a quadrilateral divides one diagonal in the ratio $$1: 2 .$$ Can it be a parallelogram?

$$ABCD$$ is a parallelogram. If $$P$$ be a point on $$CD$$ such that $$AP = AD$$ , then the measure of $$\angle P A B + \angle B C D$$ is

In a parallelogram $$ABCD$$, the diagonals intersect at $$O$$, if $$OA=3y-4$$ and $$OC=y+20$$ then $$y=$$

If $$PQRS$$ is a parallelogram and $$M$$ is a point on $$PQ$$ such that $$PM=\dfrac{3}{4}PQ$$ then find the $$ar(PQR)$$ if$$ar(PMRS)=28\ cm^{2}$$

$$x, y$$ are the mid-points of opposite sides $$AB$$ and $$DC$$ respectively of a parallelogram $$ABCD, AY$$ and $$DX$$ are intersecting at $$S, CX$$ and $$BY$$ are intersecting at $$R$$. Then $$SXRY$$ is a _