Question

for a project work , a student uses a rectangular card board ABCD as shown in figure with AB = 14cm, BC = 7cm. By a scissors,she cuts a quarter circle BFEC and semicircle DGE from it and uses the remaining part in making a cap. calculate the area of the remaining part of the rectangle .​

Answer 1

The area of remaining rectangle is 40.25 sq. cm.

• The area of rect ABCD is 14 x 7 = 98 sq cm.
• The radius of quarter circle BFEC is 7 cm.
• The area of this quarter circle BFEC is ( πr^2/4 )  =>  (3.14 * 7 * 7) / 4  => 38.5 sq cm.
• The radius of semicircle DGE is 3.5 cm.
• The radius of semicircle DGE is ( πr^2/2 )  =>  (3.14 * 3.5 * 3.5) / 2   =>  19.25 sq cm.
• Total area used   =>   ar (quarter circle BFEC) + ar (semi circle DGE)   =>   38.5 sq cm + 19.25 sq cm.  =>   57.75. sq cm
• Area remaining  =>  40.25 sq cm.

Answer 2

area of remaining rectangle is 40.25 sq. cm.

The area of rect ABCD is 14 x 7 = 98 sq cm.

The radius of quarter circle BFEC is 7 cm.

The area of this quarter circle BFEC is ( πr^2/4 )  =>  (3.14 * 7 * 7) / 4  => 38.5 sq cm.

The radius of semicircle DGE is 3.5 cm.

The radius of semicircle DGE is ( πr^2/2 )  =>  (3.14 * 3.5 * 3.5) / 2   =>  19.25 sq cm.

Total area used   =>   ar (quarter circle BFEC) + ar (semi circle DGE)   =>   38.5 sq cm + 19.25 sq cm.  =>   57.75. sq cm

Area remaining  =>  40.25 Sq. un