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UKMT Grey Kangaroo, 2025

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

In the quadrilateral PQRSPQRS, the points MM and NN are marked on sides PQPQ and RSRS respectively so that PM=MQPM = MQ and SN=2NRSN = 2NR. The area of triangle MQRMQR is 2m22\text{m}^2, and the area of triangle PSNPSN is 6m26\text{m}^2. What is the area of quadrilateral PQRSPQRS?

(A) 13 m213\text{ m}^2 (B) 14 m214\text{ m}^2 (C) 15 m215\text{ m}^2 (D) 16 m216\text{ m}^2 (E) 17 m217\text{ m}^2

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