Question

PQRS is a parallelogram. X and Y are mid-points of sides PQ and RS respectively. If W and Z are points on intersection of SX & PY and XR & YQ respectively, then show that area (triangle YWZ) = area (triangle XWZ)

Answer 1

Given PQRS is a parallelogram.X and Y are mid points of PQ and SR respectively and PS∥XY∥QR
Construction Draw SM⊥PQ

Now area∥gmXQRYarea ∥gmPQRS= XQ×SMPQ×SM=12PQPQ=12
∴ area ∥gm X Q R Y = 12 a r e a ∥ g m P Q R S = 12 × 24 c m 2 = 12 c m 2

N o w area∥gmXQYSarea∥gmXQRY = XQ×SMXQ×SM = 1
∴ a r e a ∥ g m X Q Y S = a r e a ∥ g m X Q R Y = 12 c m 2

Note:- Height is same for all parallelograms as they are between the same parallel lines.

Answer 2

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