Question

An rectangle is inscribed inside a circle,whose length is 8cm and breadth is 6cm. What is the area of the circle?​

Answer 1

GIVEN:

A rectangle is inscribed inside a circle,

Length of rectangle = 8 cm

Breadth = 6 cm

TO FIND:

Area of the circle

SOLUTION:

In rectangle ABCD,

Length = 8 cm, breadth = 6 cm. [Given]

Consider triangle ABC,

where AB² + BC² = AC² [Pythagoras theorem]

==> AC² = 8² + 6²

==> AC² = 64 + 36

==> AC = √100

==> AC = 10 cm

∴ Diameter of the circle (AC) = 10 cm

Area of the circle = πr²

= 3.14 × 10/2 × 10/2

= 314/4

= 78.5

∴ Required area of circle is 78.5 cm²

Answer 2

Required answer :-

Question :

➣ An rectangle is inscribed inside a circle,whose length is 8cm and breadth is 6cm. What is the area of the circle?

Solution :

Given,

➣ Length of rectangle = 8 cm

➣ Breadth of rectangle = 6 cm

To find:

➣ Area of the circle

Formulas used:

➣ Area of rectangle = Length (L) × Breadth (b)

➣ Area of circle = πr²

Let,

AB be length of the given rectangle and,

BC be breadth of rectangle.

Therefore,

AB = 8 cm

BC = 6 cm

Step by step explaination : ________________________________

First, we have to calculate the value of side CA that is the hypotenuse of the triangle CAB.

That is,

(Hypotenuse)² = (Base)²+(Perpendicular)²

AC² = AB² + BC²

AC² = (8)² + (6)²

AC² = 64 + 36

AC² = 100

AC = √100

AC = 10

Thus the length of side AC is 10 cm.

Now, we have to calculate radius of the circle.

That is,

Radius of circle = AC / 2

Radius = 10/2

Radius = 5 cm

Thus radius of the given circle is 5 cm.

Now we have to calculate the area of circle.

That is,

Area of circle = πr²

= (22/7) × (5)²

= 78.57 cm²

Thus area of circle is 78.57 cm²

_______________________________