### Video Transcript

Using 3.14 to approximate π and
the fact that π΄π΅πΆπ· is a square, calculate the perimeter of the shaded part.

At first, it may seem that the
perimeter of this shaded region will be tricky to work out as itβs an unusual
shape. If we look carefully though, we see
that each of these unshaded portions are quarter circles. The shaded region is enclosed by
the curved portions of these four quarter circles. Each of these arc length is
one-quarter of the circumference of a circle, but as there are four of them,
together they form the full circumference of a circle.

We know that the formula for
calculating the circumference of a circle is πΆ equals ππ, where π represents the
circleβs diameter. So the question is, what is the
diameter of this circle?

Considering the quarter circle in
the bottom left of the figure, we can see that the radius of this circle will be
half of the side length of the square. Thatβs 68 over two. So the radius is 34
centimeters. The diameter of a circle is twice
the radius, so the diameter is two times 34; itβs 68 centimeters. In fact, we could have deduced this
from the figure without halving and then doubling again. Two of the radii of the quarter
circles lie along the side length of the square, so twice the radius is 68
centimeters. And as the diameter is twice the
radius, we find again that the diameter is 68 centimeters. Weβve already said that the
perimeter of the shaded region is equal to the circumference of the full circle made
up of these four quarter circles.

So using the formula πΆ equals
ππ, we find that the perimeter of the shaded region is π multiplied by 68. Weβre told in the question to use
3.14 as an approximation for π. So multiplying gives 213.52. The units for this perimeter are
the same as the length units used in the question. So we find that the perimeter of
the shaded part using 3.14 as an approximation for π is 213.52 centimeters.