Question

4) Two identical rectangles with sides of length 3 cm and 9 cm are
overlapping as in the diagram.
What is the area of the overlap of the two rectangles?
A) 12cm square
B) 13.5cm square
C) 14cm square
D) 15cm square
E) 16cm square ​

Answer 1

For Sector PQXR , PQ = QR = 4 cm

now for the sector PYRQ = PR= PQ = 4cm

therefore in triangle PQR , PQ = QR =PR = 4cm

∴ Δ PQR is an equilateral triangle and have side of 4cm

∴∠PQR =∠QPR =∠PRQ = 60°

now the area of shaded portion = 2× area of PYRXQP

=( area of sector PQXRMP + area of segment PYMPR)

2(60°/360°×π(4)² + area of sector PQNRYP - area of Equilateral triangle PQR)

=2( 60°/360°×π×16 +60°/360°×π×16 -√3/4×16)

=2(2×1/6×π×16 -4√3)

=2(16/3×3.141-4×1.732)     ( ∵π = 3.141 and √3 = 1.732 )

=2×(16.75-6.92)

=2×9.82

=19.64cm²

Hence the shaded portion = 19.64cm²