Find the area of shaded trapezium if the area of the rectangle is 4800 cm^{2} and the area of ΔAPD is 300 cm^{2}.

- 3400 cm
^{2} - 4200 cm
^{2} - 4800 cm
^{2} - 5100 cm
^{2}

Option 2 : 4200 cm^{2}

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Given,

Area of rectangle ABCD = 4800 cm^{2}

⇒ 4800 = Length × breadth

⇒ AD = BC = 4800/80 = 60 cm

Area of ΔAPD = 300 cm^{2}

As ΔAPD is right angled triangle –

⇒ Area of ΔAPD = 1/2 × AP × AD

⇒ 300 = 1/2 × AP × 60

⇒ AP = 10 cm

Then, BQ = 10cm

⇒ PQ = 80 – 10 – 10 = 60cm

Area of trapezium PQCD

= 1/2 × (sum of parallel side) × Distance between them

= 1/2 × (60 + 80) × 60

= 4200 cm^{2}

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