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 π΄π is the same length as line
segment ππ·. From this, we can deduce that the
diagonals of the rhombus, thatβs ππ and ππ, are each parallel to one side of the
rectangle. And so it follows that theyβre also
the same length as the rectangle sides. So ππ is 15.8 centimeters and
ππ 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
π one and π two, then the area of a rhombus is π one multiplied by π two over
two. So the area of the rhombus ππππ
is equal to the length of ππ multiplied by the length of ππ over two. Thatβs 30.3 multiplied by 15.8 over
two, which is 293.37 square centimeters.
