Question

ABCD is a rectangle, where AB = 4 cm and AD = 2 cm. Two arcs are drawn of radius AD and BC respectively. What is the area of the shaded region?

• A. $4 – π$cm^2$$
• B. $8 – π$cm^2$$
• C. $4 – 2π$cm^2$$
• D. $8 – 2π$cm^2$$

Answer 1

Answer:

$8 – 2π$cm^2$$

Given:

⇒ Length of the rectangle = 4 cm

⇒ Breadth of the rectangle = 2 cm

Calculation:

∴ Area of the rectangle = $4\times{2}=8cm^2$

⇒ Area of the arc having radius AD,

$⇒\frac{1}{4}\times{π}\times{22}$

$⇒πcm^2$

⇒ Area of the arc having radius BC,

$⇒\frac{1}{4}\times{π}\times{22}$

$⇒πcm^2$

∴ Area of the shaded region,

⇒8-2π $cm^2$