A rhombus has sides of 5 cm and one diagonal is 6 cm long. Find the area of the rhombus.
To find the area of a rhombus, you can use the formula:
Area = (Diagonal1 * Diagonal2) / 2
Given that one diagonal is 6 cm long, and we know that the sides of the rhombus are 5 cm, we can find the length of the other diagonal.
In a rhombus, the diagonals are perpendicular to each other and bisect each other. This means that each diagonal divides the rhombus into two congruent right-angled triangles.
Let's use the Pythagorean theorem to find the length of the other diagonal.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In our case, one of the right-angled triangles has one leg equal to half of one side of the rhombus (which is 5 cm), and the hypotenuse is the given diagonal (6 cm).
Using the Pythagorean theorem, we can calculate the other leg (the length of the other diagonal):
a^2 + b^2 = c^2
(5/2)^2 + b^2 = 6^2
25/4 + b^2 = 36
b^2 = 36 - 25/4
b^2 = 144/4 - 25/4
b^2 = 119/4
b = sqrt(119)/2
Now that we have the length of both diagonals, we can find the area of the rhombus.
Area = (Diagonal1 * Diagonal2) / 2
Area = (6 cm * sqrt(119)/2) / 2
Area = 3 cm * sqrt(119)/2
Therefore, the area of the rhombus is 3 cm * sqrt(119)/2.