SOLUTION: Find the area of a circle inscribed in a rhombus whose perimeter is 100 cm, and whose longer diagonal is 40 cm.

Question 255604: Find the area of a circle inscribed in a rhombus whose perimeter is 100 cm, and
whose longer diagonal is 40 cm.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Since the perimeter is 100 the sides are 25 each.
The diagonals are perpendicular and meet in the center of the circle.
There is a right triangle with a side of 40/2=20 and hypotenuse of 25.
20^2+b^2=25^2
400+b^2=625
b^2=225
b=15
(15*20)/2=150 sq cm Area of triangle.
Draw a line from the right angle, which is also the center of the circle, perpendicular to the hypotenuse and label it x.
25x/2=150
25x=300
x=12 radius of the circle.
pi*12^2=144pi sq cm area of the circle.
.
Ed
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