The length of a side of a rhombus is 4.1 cm and one of its diagonals is 1.8 cm. Find the area of the rhombus.
Answers
Answer:
The area of Rhombus is 7.2cm²
Step-by-step Explanations :
( Please see the attached document for diagram )
Given : length of side = 4.1cm
Length of diagonal (D1) = 1.8cm
To find : Area of Rhombus = ?
In rhombus all side is equal therefore,
AC = 1.8cm -------- (given)
CD = AD = AB = BC = 4.1cm
O is mid point of AC,
So,
OC = AC/2 = 1.8/2 = 0.9cm
OB² = BC² - OC²
Substituting the given value in above equation we get,
OB² = (4.1)² - (0.9)²
= 16.81 - 0.81
= 16
OB² = 16
∴ OB = 4 ------- ( By taking square root on both the sides )
So, DB = 2 × OB = 4×2 = 8 cm
We know that,
Area of Rhombus = 1/2 × D1 × D2
Substituting the value in above formula we get,
Area of Rhombus = 1/2 × 1.8 × 8
= 7.2cm²
Hence the Area at Rhombus = 7.2cm²
Area of the rhombus is 7.2 cm²
Given:
- A rhombus
- Length of side = 4.1 cm
- One Diagonal = 1.8 cm
To Find:
- Area of the Rhombus
Solution:
- Rhombus has 4 sides of Equal length
- Area of Rhombus = (1/2) x Product of Diagonals
- 4 x (side)² = (diagonal 1)² + ( diagonal 2)²
Step 1:
Use 4 x (side)² = (diagonal 1)² + ( diagonal 2)² and substitute side = 4.1 and Diagonal 1 = 1.8 cm
4 ( 4.1)² =1.8² + (diagonal 2)²
=> 67.24 + 3.24 + (diagonal 2)²
=> 64 = (diagonal 2)²
=> diagonal 2 = 8 cm
Step 2:
Use formula for Area of Rhombus = (1/2) x Product of Diagonals
Area = (1/2) (1.8)(8)
=> Area = 7.2 cm²
Area of the rhombus is 7.2 cm²