A ** rhombus ** is a parallel with four congruent sides. The many of rhombus is ** rhombi ** . (I love the word.)

The formula because that the area that a rhombus is the very same as the formula because that a parallelogram:

A = b h ,

whereby b is the size of a base and also h is the height.

Area = 5 ⋅ 4 = 20 centimeter 2 .

### Diagonals that a Rhombus

If a parallel is a rhombus, then its diagonals space perpendicular.

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

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

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

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

** example 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 are 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 value of x to uncover m ∠ D A B .

every pair the opposite angles of a rhombus is congruent. So,

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

** instance 2: **

In rhombus X Y Z W , m ∠ W Y Z = 63 ° . Discover m ∠ Y Z V .

The diagonals the 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 solve.

m ∠ Y Z V + 90 ° + 63 ° = 180 °

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

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