You are here
Question 5 - Paralleograms & triangles with same base & same parallel lines - Areas of Parallelograms and Triangles
Last updated at August 14, 2026 by Teachoo
Paralleograms & triangles with same base & same parallel lines
Areas of Parallelograms and Triangles
Concept wise
- Introduction
- Paralleograms with same base & same parallel lines
- Triangles with same base & same parallel lines
-
Paralleograms & triangles with same base & same parallel lines
- Median divides triangle into two triangles of equal area
Transcript
Question 5 In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) ar (PQRS) = ar (ABRS) Since PQRS is a parallelogram PQ ∥ RS & ABRS is also a parallelogram So, AB ∥ RS Since PQ ∥ RS & AB ∥ RS We can say that PB ∥ RS Now, PQRS & ABRS are two parallelograms with the same base RS and between the same parallels PB & RS ∴ ar (PQRS) = ar (ABRS) Question 5 In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (ii) ar (AXS) = 1/2 ar (PQRS) Since ABRS is a parallelogram, AS ∥ BR Δ AXS and parallelogram ABRS lie on the same base AS and are between the same parallel lines AS and BR, ∴ Area (ΔAXS) = 1/2 Area (ABRS) ⇒ Area (ΔAXS) = 1/2 Area (PQRS) Hence proved
