Question

find area of the circle?​

Answer 1

Given:

A rectangle inscribed within a circle.

The dimensions of the rectangle is 3 cm by 4cm.

To Find:

The area of the circle.

Recall:

• All sides of the rectangle are 90°, therefore it makes it possible to apply Pythagoras theorem using two of its sides and its diagonal.
• The diagonal of the rectangle is the dimeter of the circle.

Formula needed:

• $a^2 + b^2 = c^2$
• $\text{Area of a circle } = \pi r^2$

Solution:

Find the dimeter of the circle:

Diameter = diagonal of the circle

The 2 sides of the rectangle are 3 cm and 4 cm

$a^2 + b^2 = c^2$

$c^2 = 3^2 + 4^2$

$c^2 = 9 + 16$

$c^2 =25$

$c = 5$

Find the radius of the circle:

$\text{Radius } = \text {Diameter} \div 2$

$\text{Radius } = \text {5} \div 2$

$\text{Radius } = 2.5 \text{ cm}$

Find the area of the circle:

$\text{Area of a circle } = \pi r^2$

$\text{Area of the circle } = \pi (2.5)^2$

$\text{Area of the circle } = 6.25 \pi \text{ cm}^2$

$\text{Area of the circle } = 19.64 \text{ cm}^2$

$\text{Answer: 19.64 cm}^2$