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perimeter PQUV = 46cm
since RSTU is a square
UT = ST = RU = 6cm
QU (breadth of rectangle) = QR + RU = 4 + 6 = 10cm
PQ is the length of rectangle
2 length + 2 breadth = perimeter
2 length + 2 breadth = 46 1 length + 1 breadth = 46 ÷ 2 = 23
1 breadth (QU) → 10 1 length (PQ) → 23 - 10 = 13 cm
shaded triangle → rectangle + square - (▵ D + ▵ C + ▵ E
rectangle area → 10 x 13 = 130 cm²
square area → 6 x 6 = 36 cm²
▵ D area → 1/2 x base x height = 1/2 x 19 x 10 = 95 cm²
▵ C area → 1/2 x base x height = 1/2 x 13 x 4 = 26 cm²
▵ E area → 1/2 x base x height = 1/2 x 6 x 6 = 18 cm²
shaded triangle → rectangle + square - (▵ D + ▵ C + ▵ E = 130 + 36 - (95 + 26 + 18) = 27 cm²