Question

ABCD is a rectangle. AB = 10 cm, BC = 7 cm. The perimeter of the shaded part is ______.

पर्याय

• 12 cm

• 56 cm

• 42 cm

• 48 cm

Answer 1

ABCD is a rectangle. AB = 10 cm, BC = 7 cm. The perimeter of the shaded part is 42 cm.

Explanation:

Given:

• Rectangle ABCD with AB = 10 cm and BC = 7 cm.
• The shaded area consists of two semicircles inside the rectangle, one on the left and one on the right.

Step 1: Understand the geometry of the shaded part.

The two semicircles are drawn on the shorter sides BC and AD, with diameter equal to BC = 7 cm.

Radius (r) of each semicircle = `"BC"/2`

= `7/2`

= 3.5 cm

Step 2: Calculate the perimeter of the shaded part.

The shaded region includes two semicircular arcs each half the circumference of a circle with radius 3.5 cm.

Total arc length of two semicircles 

= Circumference of one full circle 

= 2πr 

= `2 xx 22/7 xx 3.5` 

= 22 cm

The top and bottom straight lines connecting these two arcs are AB and DC, each = 10 cm.

So, total perimeter of shaded part

= Length of top + Length of bottom + Arc length of semicircles 

= 10 + 10 + 22

= 42 cm