Use 3.14 to approximate 𝜋 and calculate
the perimeter of the figure.
In this question, we’ve been asked to
calculate the perimeter of a composite figure which looks a little bit like an ice cream
cone. We have a semicircle which sits on top of
a triangle. Notice that the dividing line between
these two shapes — that’s the third side of the triangle or the straight edge of the
semicircle — is not part of the perimeter because it isn’t part of the outside of the full
figure. The perimeter is composed of the
semicircular arc and two of the sides of the triangle.
We can see from the figure indicated by
these lines here that the triangle is equilateral. All of its sides are the same length. So the two straight edges are each 35
centimeters long. For the semicircular arc, we recall that
the circumference of a full circle is 𝜋 times the diameter. So the length of the semicircular arc
will be half of this. It’s 𝜋𝑑 over two. The diameter of this circle is the same
as the side length of the triangle. It’s 35 centimeters. So the semicircular arc length is 35𝜋
over two or 35 over two 𝜋.
Now we’re told in the question that we
need to use 3.14 as an approximation for 𝜋. So our perimeter is 35 over two
multiplied by 3.14 plus 35 plus 35. To work out 35 over two multiplied by
3.14 without a calculator, we can first divide 3.14 by two to give 1.57 and then multiply 35
by 1.57 using any multiplication method we’re comfortable with. Here I’ve used the grid method, to find
that 35 multiplied by 1.57 is equal to 54.95. So we have 54.95 plus 70 — that’s 35 plus
35 — which is equal to 124.95. And the units for this perimeter are the
same as the units for the lengths in the question. They’re centimeters.
Because we used 3.14 to approximate 𝜋
then, there was no need for a calculator in this question. Although we did have some reasonably
tricky decimal calculations to work out.