Question

Find the area of shaded trapezium if the area of the rectangle is 4800 cm2 and the area of ΔAPD is 300 sq.cm.

• A. 3400 sq.cm
• B. 4200 sq.cm
• C. 4800 sq.cm
• D. 5100 sq.cm

Answer 1

Answer:

B. 4200 sq.cm

Given,

Area of rectangle ABCD = 4800 cm²

⇒ 4800 = $Length\times{breadth}$

⇒ AD = BC =$\frac{4800}{80} = 60 cm$

Area of ΔAPD = 300 cm²

As ΔAPD is right angled triangle –

⇒ Area of ΔAPD =$\frac{1}{2}\times{AP }\times{AD}$

⇒ 300 =$\frac{1}{2}\times{AP}\times{60}$

⇒ AP = 10 cm

Then, BQ = 10cm

⇒ PQ = 80 – 10 – 10 = 60cm

Area of trapezium PQCD

= $\frac{1}{2}\times{(sum of parallel side)}\times{(Distance between them)}$

=$\frac{1}{2}\times{(60 + 80)}\times{60}$

= 4200 cm²