###### Asked in Math and Arithmetic

Math and Arithmetic

# How do I find a missing diagonal in a rhombus?

## Answer

###### Wiki User

###### June 14, 2015 12:19PM

A rhombus has 2 diagonals and they are a straight lines drawn opposite to its interior corners intersecting each other at right angles.

###### Wiki User

###### June 14, 2015 8:51AM

The answer depends on what information you do have about the
rhombus. Assuming that you know the length of the sides and one of
the diagonals, then,

- In the triangle formed by the given diagonal and the sides of
the rhombus, you know all three sides. So you can use the cosine
rule to calculate the angle between the sides of the
rhombus.
- The other pair of angles in the rhombus are its
supplement.
- So now you know two sides and the included angle of the
triangle formed by the missing diagonal and the sides of the
rhombus.
- You can use the cosine rule again to find the missing diagonal.

## Related Questions

###### Asked in Geometry, Math and Arithmetic, Algebra

### The diagonals of the rhombus are in the ratio 3 4 the perimeter of the rhombus is 40cm find the lengths of the sides and of the diagonals?

The length of the sides of the rhombus are 10cm, as a rhombus
has equal sides.
since the diagonals of a rhombus are perpendicular,
ratio of
side of rhombus to
1/2 a diagonal to
1/2 of another diagonal
is 5:4:3 (pythagorean thriple),
hence ratio of side of rhombus to
1 diagonal
to another diagonal
is 5:8:6.
since 5 units = 10cm
8 units = 16cm
6 units = 12cm
and there are your diagonals.

###### Asked in Math and Arithmetic, Algebra, Geometry

### What is the missing diagonal of a rhombus if the area is 120ft2 and the other diagonal is 16 feet?

Given:
The area of the rhombus is 120 square feet
The diagonal of the rhombus is 16 feet
think of the rhombus being two identical triangles, connected at
their base which is 16 feet long. Each of them would then have an
area of 60 feet.
Now, in a triangle, area = (base * height) / 2
the area is already given as 60, and the base as 16
we can say then:
60 = (16 * h) / 2
∴60 = 8h
∴h = 7.5
Now, that 7.5 is half the length of the rhombus (as it's the
height of one of our triangles, which each are half our rhombus).
So we know that that the other diagonal on the rhombus is twice
that.
In other words, the answer is 15.

###### Asked in Math and Arithmetic, Algebra, Geometry

### Find the area of a Rhombus whose side is 6cm and altitude is 4cm. If one of the diagonal is 8cm long find the length of the other diagonal?

Rhombus Area = side x height = 6 cm x 4 cm = 24 cm2
In the right triangle formed by the side and the height of the
rhombus, we have:
sin (angle opposite to the height) = height/side = 4 cm/6cm = 2/3,
so that
the angle measure = sin-1 (2/3) ≈ 41.8⁰.
In the triangle formed by two adjacent sides and the required
diagonal, which is opposite to the angle of 41.8⁰ of the rhombus,
we have: (use the Law of Cosines)
diagonal length = √[62 + 62 -2(6)(6)cos 41.8⁰] ≈ 4.3
Thus, the length of the other diagonal of the rhombus is about 4.3
cm long.

###### Asked in Math and Arithmetic, Algebra, Geometry

### There is a yellow rhombus on the flag of Brazil The long diagonal on the rhombus measures 7.0 units The short diagonal on the rhombus measures 4.4 units The area of any rhombus is half the product?

That is one of the ways of finding the area of a rhombus. The
area is half the product of the diagonals. In this case, 1/2 of 7 x
4.4 or .154. You can also find the area of a rhombus by using one
side as the base and finding an altitude for that base and
multiplying them. There is a third way using trigonometry.