Theory question 104
Mensuration of Plane ShapesIn the diagram, PQRS is a quadrilateral, ∠PQR = ∠PRS = 90°, |PQ| = 3 cm, |QR| = 4 cm and |PS| = 13 cm. Find the area of the quadrilateral.
Show the model answer
Model answer
In ΔPQR: |PR| = √(32 + 42) = 5 cm
In ΔPRS: |RS| = √(132 − 52) = √144 = 12 cm
Area = ½ × 3 × 4 + ½ × 5 × 12 = 6 + 30
Area = 36 cm2
Explanation
Split the quadrilateral along PR into two right-angled triangles.