Question

Find the area of a parallelogram PQRS, if PR=24cm and QU=ST=8cm.

Answer 1

area of parallelogram PQRS = area of triangle PQR + area of triangle PSR

given,
length of QU = altitude of triangle PQR = 8cm
length of ST = altitude of triangle PSR = 8cm
length of PR = base of triangle PQR/PSR = 14cm

so, area of triangle PQR = 1/2 × length of PR × length of QU
= 1/2 × 24cm × 8cm = 12cm × 8 cm
= 96 cm²

area of triangle PSR = 1/2 × length of PR × length of ST
= 1/2 × 24cm ×8 cm = 96 cm²

hence , area of PQRS = 96 cm² + 96 cm²
= 192 cm²

Answer 2

Dear student,

Solution : In given parallelogram PQRS, you will easily see two right angle triangle Δ RSP and Δ RQP.

Area of PQRS = ar(Δ RSP) + ar(Δ RQP)

area of right angle triangle be easily calculated by = 1/2 X base X height

Area of PQRS = 1/2 (PR)(ST) + 1/2(PR)(QU)

Area of PQRS = 1/2 (24)(8) + 1/2(24)(8)

Area of PQRS =96+96

Area of PQRS = 192 cm-sq

Hope it helps you.