Question

determine the perimeter and area of the Shaded portion of the figure below given the Circle diameter of 7 centimetre and the perimeter of the entire figure is 42 centimetre ​

Answer 1

perimeter = 43.98cm

area = 76.96cm^2

Explanation:

You take into account that the shaded regions are perfect circles, then, the total perimeter of the shaded regions are given by the circumference of both circles.

You calculate the circumferences, by using the following formula:

`C=2\pi r` (1)

r: radio of the circles = (7/2)cm = 3.5cm

The total perimeter is twice the value of C in the expression (1). You replace r in (1), and calculate the total perimeter:

`C=2\pi (3.5cm)=21.99cm\\\\C_T=2C=2(21.99cm)=43.98cm`

The perimeter of the shaded region is 43.98cm.

The area of the shaded region is twice the area of one of the circle, which is given by:

`A=\pi r2=\pi (3.5cm)^2=38.48cm^2\\\\A_T=2A=2(38.48cm^2)=76.96cm^2`

The total area of the shaded region is 76.96cm^2