Area of parallelogram and triangle = |a × b| and ½|a × b|समांतर चतुर्भुज और त्रिभुज का क्षेत्रफल = |a × b| और ½|a × b|Parallelogram aur triangle ka area = |a × b| aur ½|a × b|

NCERT Fig 10.26–10.27 · Class 12 Maths · Chapter 10 · interactive diagram

Parts and what they mean

• Side \vec{a} (base) (भुजा \vec{a} (आधार)) — Base length |\vec{a}|.
• Side \vec{b} (भुजा \vec{b}) — The adjacent side from the same vertex.
• Height = |\vec{b}|\sin\theta (ऊँचाई = |\vec{b}|\sin\theta) — Perpendicular from the tip of \vec{b} to the base.
• Parallelogram area = |\vec{a} \times \vec{b}| (समांतर चतुर्भुज का क्षेत्रफल = |\vec{a} \times \vec{b}|) — base × height = |\vec{a}|\,|\vec{b}|\sin\theta = |\vec{a} \times \vec{b}|.
• Triangle area = \dfrac12|\vec{a} \times \vec{b}| (त्रिभुज का क्षेत्रफल = \dfrac12|\vec{a} \times \vec{b}|) — The diagonal cuts the parallelogram into two equal triangles.
• Angle θ (कोण θ) — Angle between the sides at the common vertex.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 10.26–10.27. Report a mistake