Video Transcript
Determine the area of the rhombus
𝐴𝐵𝐶𝐷. Unit length equals one
centimeter.
On the coordinate grid, we have
this rhombus 𝐴𝐵𝐶𝐷. As it’s a rhombus, we know that the
four sides will all be of the same length. We’re asked to find the area of
this rhombus, which is the amount of space within the shape. When we’re finding the area of a
rhombus, we have a choice of two different formulas. The first formula for the area of a
rhombus tells us that we multiply the two diagonals and divide by two. With the second formula, we would
have the base multiplied by the perpendicular height.
In order to establish which area
formula we should use, we’ll need to look and see which lengths we’re given. In order to use the second formula,
the base would be the length of one of the sides, and we need to find the
perpendicular height. As we’re not going to be physically
measuring these lengths with a ruler, we’d need to use something like the
Pythagorean theorem to find these lengths.
Let’s see if it would be easier to
use our first formula. Could we find the length of the
diagonals? Well, yes, we can, using the
grid. Our horizontal line 𝐴𝐶 goes from
negative eight to two on the 𝑥-axis, which means that it will be 10 units long. In fact, we’re told that each unit
is one centimeter. So, 𝐴𝐶 will be 10
centimeters. The diagonal 𝐷𝐵 goes from
negative five to negative nine on the 𝑦-axis, so it will be four centimeters
long. Using the formula that involves the
diagonals, we plug in our two values, which gives us 10 multiplied by four over
two. We can simplify this first or work
out 10 times four is 40 divided by two, which gives us 20. And the units here will be the
square units of squared centimeters. We can give our answer that the
rhombus 𝐴𝐵𝐶𝐷 has an area of 20 square centimeters.
