Video Transcript
Determine the area of the rhombus
๐ด๐ต๐ถ๐ท. Unit length equals one
centimeter.
Weโre 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. Itโs equal to half of their
product.
If we denote the lengths of the
diagonals of a rhombus as ๐ one and ๐ two units, then this can be expressed using
the formula area of rhombus equals a half ๐ one ๐ two. Letโs see if we can identify the
lengths of this rhombusโs diagonals from the figure.
The two diagonals are the line
segments connecting vertices ๐ด and ๐ถ and vertices ๐ต and ๐ท. 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 ๐ด
and ๐ถ is 10 squares and hence 10 centimeters long. The diagonal connecting vertices ๐ต
and ๐ท is four centimeters long.
Substituting these values into the
formula gives that the area of rhombus ๐ด๐ต๐ถ๐ท is equal to a half multiplied by 10
multiplied by four. Thatโs a half multiplied by 40, or
a half of 40, which is 20. Recalling that the length units are
centimeters, weโve found that the area of rhombus ๐ด๐ต๐ถ๐ท is 20 square
centimeters.