Video Transcript
Determine the area of the rhombus
𝐴𝐵𝐶𝐷. Unit length equals one
centimeter.
We’re asked to find the area of
this rhombus, which has been drawn on a centimeter square grid. We recall that the area of a
rhombus can be calculated using the lengths of its diagonals. It’s equal to half of their
product.
If we denote the lengths of the
diagonals of a rhombus as 𝑑 one and 𝑑 two units, then this can be expressed using
the formula area of rhombus equals a half 𝑑 one 𝑑 two. Let’s see if we can identify the
lengths of this rhombus’s diagonals from the figure.
The two diagonals are the line
segments connecting vertices 𝐴 and 𝐶 and vertices 𝐵 and 𝐷. These line segments are horizontal
and vertical. As each square on the coordinate
grid is of length one centimeter, we can determine the length of each of these
diagonals by counting the squares. The diagonal connecting vertices 𝐴
and 𝐶 is 10 squares and hence 10 centimeters long. The diagonal connecting vertices 𝐵
and 𝐷 is four centimeters long.
Substituting these values into the
formula gives that the area of rhombus 𝐴𝐵𝐶𝐷 is equal to a half multiplied by 10
multiplied by four. That’s a half multiplied by 40, or
a half of 40, which is 20. Recalling that the length units are
centimeters, we’ve found that the area of rhombus 𝐴𝐵𝐶𝐷 is 20 square
centimeters.
