### Video Transcript

A diagonal of a rhombus has length
2.1, while the other one is four times as long. What is its area?

We start by remembering that a
rhombus is a quadrilateral with all four sides equal in length. So, when we model our rhombus,
we’ll need to have four equal sides. Instead of being given any
information about the length of the sides of this rhombus, we’re given information
about the diagonals. We’re given that one of these
diagonals has a length of 2.1 units, and the other one is four times as long. Four multiplied by 2.1 will give us
8.4. Looking at our diagram, we can see
that there’s a shorter diagonal and a longer diagonal. And therefore, the shorter one will
be 2.1 units, and the longer one will be 8.4 units.

There are two formulas that we can
use to find the area of a rhombus. One involves the base and the
perpendicular height, and the other one involves the diagonals. As we’re only given the length of
the diagonals here, it would be sensible to use that formula. So, we remember that the area of a
rhombus is equal to 𝑑 sub one multiplied by 𝑑 sub two over two, where 𝑑 sub one
and 𝑑 sub two are the lengths of the two diagonals. We can plug in the values of our
two diagonals to give us 2.1 multiplied by 8.4 over two.

Simplifying our calculation, we’ll
need to work out 2.1 multiplied by 4.2, which we can do without a calculator. We work out 21 multiplied by 42
using whatever multiplication method we choose. And then, as our two values had a
total of two decimal places, then so will our answer. We weren’t given any length units
in the question, but as we’ve worked out an area, we would be using square
units. And so, our answer is that the area
of this rhombus is 8.82 square units.