Find the area of a rhombus if the measure of each side is 26 cm and one of its diagonals is 48 cm.
Answers
Answer:
- Area of a rhombus is 480 cm².
Step-by-step explanation:
Given that:
- The measure of each side of a rhombus is 26 cm.
- One of its diagonals is 48 cm.
To Find:
- Area of a rhombus.
Formula used:
- Q = 2 × √{a² - (P/2)²}
- A = (P × Q)/2
Here,
- a = Side of a rhombus
- P = One of the diagonal of a rhombus
- Q = Other diagonal of a rhombus
- A = Area of rhombus
First finding the other diagonal of rhombus:
⟶ Q = 2 × √{26² - (48/2)²}
⟶ Q = 2 × √{26² - 24²}
⟶ Q = 2 × √{676 - 576}
⟶ Q = 2 × √{100}
⟶ Q = 2 × 10
⟶ Q = 20
∴ Other diagonal of a rhombus = 20 cm
Now finding the area of a rhombus:
⟶ A = (48 × 20)/2
⟶ A = 960/2
⟶ A = 480
∴ Area of a rhombus = 480 cm²
Answer:
Given :-
- The measure of each side is 26 cm and one of its diagonal is 48 cm.
To Find :-
- What is the area of the rhombus.
Formula Used :-
➲ Area of Rhombus = d₁ × d₂/2
where,
- d₁ = One diagonal
- d₂ = Other diagonal
Solution :-
First, we have to find the other diagonal of rhombus :
By using Pythagoras theorem we get,
↦ (BO)² + (AO)² = (BA)²
↦ (BO)² = (BA)² - (AO)²
↦ (BO)² = (26)² - (24)
↦ (BO)² = 676 - 576
↦ (BO)² = 100
↦ BO = √100
➦ BO = 10 cm
Then, BO = 10 × 2 = 20 cm
Hence, it's other diagonal is 20 cm.
Now, we have to find the area of the rhombus :
Given :
- d₁ = 48 cm
- d₂ = 20 cm
According to the question by using the formula we get,
⇒ Area of Rhombus = 48 × 20/2
⇒ Area of Rhombus = 48 × 10
➠ Area of Rhombus = 480 cm²
∴ The area of the rhombus is 480 cm².