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 .
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 ° .
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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