The area of a rhombus is half the product of its diagonals. Therefore, to find the area we will first find the lengths of the diagonals. Recall that the diagonals of a rhombus are perpendicular and they bisect each other.
Let's focus on the right triangle at the top-left of the diagram.
In this right triangle the measure of one leg is 3 and the length of the hypotenuse is 5 yards. We will use the Pythagorean Theorem to find the length of the other leg.
a^2+b^2=c^2
Let's substitute the corresponding values in the above formula and solve the resulting equation.
The length of the triangle's longer leg is 4. Since the diagonals bisect each other, we know that the other half of the diameter also has the length 4. We can then use the Segment Addition Postulate to find the length of the horizontal diameter.
We have found the lengths of the diagonals of the rhombus! We can now find the area of the rhombus by substituting the obtained values into the formula A= 12d_1 d_2. Let's do it!
A=1/2d_1 d_2
⇓
A=1/2(8)(6)=24
Thus, the area of the rhombus is 24 square units.
