A rhombus is a parallelogram with 4 congruent sides. The plural of rhombus is rhombi . (I love that word.) The formula for the area the a rhombus is the very same as the formula because that a parallelogram:

A = b h ,

whereby b is the length of a base and h is the height. Area = 5 ⋅ 4 = 20     centimeter 2 .

### Diagonals the a Rhombus If a parallel is a rhombus, then its diagonals room perpendicular.

because that Example: If ns Q R S is a rhombus, climate p R ¯ ⊥ Q S ¯ .

If a parallelogram is a rhombus, climate each diagonal line bisects a pair of the contrary angles.

for Example: If p Q R S is a rhombus, climate

∠ 1 ≅ ∠ 2 ,     ∠ 3 ≅ ∠ 4 ,     ∠ 5 ≅ ∠ 6 ,   and     ∠ 7 ≅ ∠ 8 .

instance 1:

In rhombus A B C D , m ∠ A B C = 2 x − 7     and also     m ∠ B C D = 2 x + 3 . Uncover m ∠ D A B . In a rhombus, consecutive interior angles space supplementary. So,

m ∠ A B C +     m ∠ B C D = 180 ° .

substitute the measures and solve for x .

2 x − 7 + 2 x + 3 = 180 ° 4 x = 184 x = 46

use the worth of x to uncover m ∠ D A B .

every pair that opposite angle of a rhombus is congruent. So,

m ∠ D A B = m ∠ B C D = 2 ( 46 ) + 3 = 95 ° .

example 2:

In rhombus X Y Z W , m ∠ W Y Z = 63 ° . Discover m ∠ Y Z V . The diagonals of a rhombus are perpendicular.

So, m ∠ Y V Z = 90 ° and Δ Y V Z isarighttriangle .

use the Angle sum Theorem.

m ∠ Y Z V + m ∠ Z V Y + m ∠ V Y Z = 180 °

instead of the measures and also solve.

m ∠ Y Z V + 90 ° + 63 ° = 180 °

m ∠ Y Z V + 153 ° = 180 ° m ∠ Y Z V = 27 °

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