Find the area of a rhombus whose one side measures 5 cm and one diagonal is 8 cm.
Solution:
Consider the Rhombus ABCD shown below:
From the above diagram we can write:
AB² = OA² + OB²
5² = OA² + 4²
OA² = 5² - 4²
OA² = 25 - 16 = 9
OA = √9
OA = 3
Since the diagonals of rhombus bisect each other then:
AC = 2OA
AC = 2 × 3 = 6 cm
Now we can find the area of the rhombus by using the formula:
Area of Rhombus = Half of the product of its diagonals
Area of Rhombus = (1/2) × (8) × (6) = 24 cm²
✦ Try This: Find the area of a rhombus whose one side measures 10cm and one diagonal is 16 cm.
From the above diagram we can write:
AB² = OA² + OB²
10² = OA² + 8²
OA² = 10² - 8²
OA² = 100 - 64 = 36
OA = √36
OA = 6
Since the diagonals of rhombus bisect each other then:
AC = 2OA
AC = 2 × 6 = 12 cm
Now we can find the area of the rhombus by using the formula:
Area of Rhombus = Half of the product of its diagonals
Area of Rhombus = (1/2) × (16) × (12) = 96 cm²
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Sample Problem 8
160 m³ of water is to be used to irrigate a rectangular field whose area is 800 m². What will be the height of the water level in the field
Summary:
The area of a rhombus whose one side measures 5 cm and one diagonal is 8 cm 24 cm²
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