Mathematics

Mathematics

Problem

Parallelogram PQRSPQRS has an area of 96 cm296\,\text{cm}^2. Diagonal PRPR is drawn. What is the area of △PQR\triangle PQR? a) 32 cm232\,\text{cm}^2 b) 48 cm248\,\text{cm}^2 c) 24 cm224\,\text{cm}^2 d) 96 cm296\,\text{cm}^2
Intuitive explanation

A diagonal of a parallelogram divides it into two congruent triangles. Since the diagonal PRPR splits parallelogram PQRSPQRS into triangles PQRPQR and PRSPRS, and these triangles have equal area, each triangle must have exactly half the parallelogram's total area.

Intuitive explanation

A diagonal of a parallelogram divides it into two congruent triangles. Since the diagonal PRPR splits parallelogram PQRSPQRS into triangles PQRPQR and PRSPRS, and these triangles have equal area, each triangle must have exactly half the parallelogram's total area.

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