Video Transcript
The figure shows a rhombus within a
rectangle. Find the area of the rhombus to two
decimal places.
Looking at the diagram, we notice
that the vertices of the rhombus are each at the midpoint of one of the rectangle
sides. We know this because these line
markers indicate that, for example, line segment 𝐴𝑋 is the same length as line
segment 𝑋𝐷. From this, we can deduce that the
diagonals of the rhombus, that’s 𝑋𝑍 and 𝑌𝑇, are each parallel to one side of the
rectangle. And so it follows that they’re also
the same length as the rectangle sides. So 𝑋𝑍 is 15.8 centimeters and
𝑌𝑇 is 30.3 centimeters.
We can then recall that the area of
a rhombus is equal to half the product of the lengths of its diagonals. If the lengths of the diagonals are
𝑑 one and 𝑑 two, then the area of a rhombus is 𝑑 one multiplied by 𝑑 two over
two. So the area of the rhombus 𝑋𝑇𝑍𝑌
is equal to the length of 𝑌𝑇 multiplied by the length of 𝑋𝑍 over two. That’s 30.3 multiplied by 15.8 over
two, which is 293.37 square centimeters.
