Question

if the area of rhombus is
$32 \sqrt{3}$
cm^2 the radius of the circle is​

Answer 1

Answer:

Explanation:

O is centre of the circle

OPQR is a rhombus.

Let the diagonals OQ and PR intersect at S

area of rhombus OPQR = 32√3 cm2

Let

OP = OQ = OR = r

OS = SQ = r/2

RS = PS

In right ΔOSP

By Pythagoras theorem

OP² = OS² + PS²  

r² = (r/2)² + PS²

PS² = r² – (r/2)²  

= 3r²/4

so, PS = (√3r/2)

PR = 2PS = √3r

area of rhombus = 1/2 x d₁ x d₂

area of rhombus OPQR = 1/2 x OQ x PR

32√3 = 1/2 x r x √3r

32 = 1/2 r²

r² = 64

r = 8

Area of circle = πr²  

= 22/7 x 8²

= 201. 14 sq cm