A rhombus has sides of 5 cm each and one diagonal is 6 cm long. Find the area of the rhombus.
the diagonals of a rhombus measure 8cm and 6cm what is the lengh of the rhombus
To find the area of a rhombus, you can use the formula: Area = (diagonal 1 * diagonal 2) / 2.
In this case, we have one diagonal measuring 6 cm. Since a rhombus has diagonals that bisect each other at a right angle, both diagonals have the same length.
Let's call each diagonal d. So, d = 6 cm.
Using the formula to find the area:
Area = (d * d) / 2
= (6 cm * 6 cm) / 2
= (36 cm^2) / 2
= 18 cm^2
Therefore, the area of the rhombus is 18 square cm.
To find the area of a rhombus, you can use the formula:
Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals of the rhombus.
In this case, we know that one diagonal is 6 cm long. However, we need to find the length of the other diagonal.
Since a rhombus has opposite sides equal in length, we can use the Pythagorean theorem to find the length of the other diagonal.
Let's label the rhombus as ABCD, with A and C being the midpoints of the diagonals.
Using the Pythagorean theorem, we can solve for the length of the other diagonal, which we'll call d2:
d2^2 = a^2 + b^2
In a rhombus, a and b are the lengths of the sides.
Since the sides of the rhombus are 5 cm each, we can substitute this into the equation:
d2^2 = 5^2 + 5^2
d2^2 = 25 + 25
d2^2 = 50
Taking the square root of both sides, we find:
d2 = √50
Now that we have both diagonals, we can find the area of the rhombus using the formula:
Area = (d1 * d2) / 2
Substituting the values, we have:
Area = (6 * √50) / 2
Area = 3 * √50
So, the area of the rhombus is 3 * √50 square cm.
make a sketch
in a rhombus, the diagonals right-bisect each other.
So we get 4 congruent right angled triangles.
By Pythagoras , it is easy to see that each triangle has sides 3,4, and 5
So the other diagonal is 8 units long.
The area of a rhombus is (1/2)(product of the diagonals)
= (1/2)(6)(8) = 24