In quadrilateral ABCD the diagonals AC and BD are perpendicular to each other, with AC = 10 units and BD = 14 units. P, Q, R and S are the midpoints of AB, BC, CD and DA respectively. What is the area of the quadrilateral PQRS?

Question

Accepted Answer

35 square units. PQ is a midline of triangle ABC, so PQ ∥ AC and PQ = 5. QR is a midline of triangle BCD, so QR ∥ BD and QR = 7. Since AC ⊥ BD, the sides PQ and QR are perpendicular, making PQRS a rectangle of dimensions 5 × 7, so its area is 35 square units.

In quadrilateral ABCD the diagonals AC and BD are perpendicular to each other, with AC = 10 units and BD = 14 units. P, Q, R and S are the midpoints of AB, BC, CD and DA respectively. What is the area of the quadrilateral PQRS?

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