Question Video: Calculating the Perimeter of a Composite Figure Involving Circles and Triangles Mathematics

Use 3.14 to approximate ๐œ‹ and calculate the perimeter of the figure.


Video Transcript

Use 3.14 to approximate ๐œ‹ and calculate the perimeter of the figure.

In this question, weโ€™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 โ€” thatโ€™s the third side of the triangle or the straight edge of the semicircle โ€” is not part of the perimeter because it isnโ€™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 ๐œ‹ times the diameter. So the length of the semicircular arc will be half of this. Itโ€™s ๐œ‹๐‘‘ over two. The diameter of this circle is the same as the side length of the triangle. Itโ€™s 35 centimeters. So the semicircular arc length is 35๐œ‹ over two or 35 over two ๐œ‹.

Now weโ€™re told in the question that we need to use 3.14 as an approximation for ๐œ‹. 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 weโ€™re comfortable with. Here Iโ€™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 โ€” thatโ€™s 35 plus 35 โ€” which is equal to 124.95. And the units for this perimeter are the same as the units for the lengths in the question. Theyโ€™re centimeters.

Because we used 3.14 to approximate ๐œ‹ then, there was no need for a calculator in this question. Although we did have some reasonably tricky decimal calculations to work out.

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