Assume a side to br x. pther will be 7-x. as the radius is 2.5. diameter which is nothing but diagonal of the recatngle is 5. 2 sides and a diagonal form a right angled triangle. use pythogoras theorem and solve for x. you get sides to be 5 and 2. so area is 10

A rectangle is inscribed in a circle with a radius of 2.5 cm. The perimeter of the rectangle is 14 cm. Find the area of the rectangle.



The first step to solve this problem is to understand the properties of a rectangle inscribed in a circle.

Properties of a Rectangle inscribed in a Circle:
- The diagonals of the rectangle are equal in length and are also the diameters of the circle.
- The length and width of the rectangle are equal to the radius of the circle.



Since the perimeter of the rectangle is given as 14 cm, we can write the equation:

2 * (Length + Width) = 14

Dividing both sides by 2, we have:

Length + Width = 7

As mentioned earlier, the length and width of the rectangle are equal to the radius of the circle, which is 2.5 cm.

So, Length = 2.5 cm and Width = 2.5 cm.



The area of a rectangle is given by the formula:

Area = Length * Width

Plugging in the values, we have:

Area = 2.5 cm * 2.5 cm

Calculating the area, we get:

Area = 6.25 cm²

Therefore, the area of the rectangle inscribed in the circle with a radius of 2.5 cm and a perimeter of 14 cm is 6.25 cm².