All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 cm². (Use π = 3.14)
Solution:
Given, all the vertices of a rhombus lie on a circle.
Area of the circle = 1256 cm²
We have to find the area of the rhombus.
From the figure,
ABCD is a rhombus whose vertices lie on a circle.
d₁ and d₂ are the diagonals of the rhombus.
Area of circle = πr²
1256 = 3.14r²
r² = 1256/3.14
r² = 400
r = 20 cm
Therefore, the radius of the circle is 20 cm
Since all the vertices of the rhombus lie on the circle. The diagonal of the rhombus is equal to the diameter of the circle.
Diameter of circle = 2(20) = 40 cm
Area of rhombus = 1/2 × d₁ × d₂
= 1/2 × 40 × 40
= 20 × 40
= 800 cm²
Therefore, the area of rhombus is 800 cm²
✦ Try This: All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 3586 cm². (Use π = 3.14).
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 12
All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 cm². (Use π = 3.14)
Summary:
All the vertices of a rhombus lie on a circle. The area of the rhombus, if the area of the circle is 1256 cm² is 800 cm²
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