Video Transcript
Which of the following shapes is a
concave polygon?
Let’s begin by reminding ourselves
what it means for a polygon to be concave. We say that a polygon is concave if
one or more of its interior angles is greater than 180 degrees. Now, this results in it looking a
little bit like some of the vertices of the shape point inwards towards its
center. Now, of course, we’re dealing
purely with polygons. And so, our shapes themselves must
have only straight sides. And this means we can instantly
disregard option (A) as being a concave polygon. It has two straight sides and one
curved side. It does, however, have one angle
greater than 180 degrees. But we disregard it because it’s
not a polygon.
And what about shape (B)? It is indeed a polygon. It’s a two-dimensional shape made
up of a number of straight sides. But actually, we identify each of
the interior angles as being less than 180 degrees. And so, we disregard option (B) as
well.
We now look at option (C). It is a polygon; again, it’s made
up of a number of straight sides. This angle here is less than 180,
as is this one, and this one. But we have two angles here which
are greater than 180 degrees. In fact, we can see they are 270
degrees. This is less than 180, as is this,
but this angle is also greater than 180 degrees. And so, the answer must be (C). (C) is a concave polygon. But let’s check option (D) and
(E).
We might recall that in a concave
polygon, one or more of its diagonals will lie outside of the shape itself. And remember, we construct the
diagonals by joining nonadjacent vertices with a straight line. The diagonals of shape (D) are
shown. All of these lie within the polygon
itself. And so, it cannot be a concave
polygon. And we disregard (D) as we
expected. Similarly, joining the nonadjacent
vertices on shape (E) with straight lines, and we see that all of those diagonals
lie inside the polygon. So (E) cannot be concave
either. And so, we’re able to confirm that
the answer is (C). Shape (C) is a concave polygon.
