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PQRS is a parallelogram.T is the mid-point of PQ and U is the mid-point of RS.N is any point on QR and M is any point on TU. Question promptWhich of these is not equal to the area of quadrilateral PMSN?Question response areaSelect one optionarea of triangle PMS area of triangle PNS area of parallelogram TQRU area of parallelogram PQRS

Question

PQRS is a parallelogram.T is the mid-point of PQ and U is the mid-point of RS.N is any point on QR and M is any point on TU. Question promptWhich of these is not equal to the area of quadrilateral PMSN?Question response areaSelect one optionarea of triangle PMS area of triangle PNS area of parallelogram TQRU area of parallelogram PQRS

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Solution

The area that is not equal to the area of quadrilateral PMSN is the area of parallelogram PQRS.

Here's why:

  1. The area of triangle PMS is equal to the area of quadrilateral PMSN because they share the same base (PM) and height.

  2. The area of triangle PNS is equal to the area of quadrilateral PMSN because they share the same base (PN) and height.

  3. The area of parallelogram TQRU is equal to the area of quadrilateral PMSN because TQRU is half of the parallelogram PQRS and PMSN is also half of the parallelogram PQRS.

  4. However, the area of parallelogram PQRS is not equal to the area of quadrilateral PMSN because PQRS is twice the size of PMSN.

This problem has been solved

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