Questions & Answers
Question
Answers

The area of two congruent circles of radii $r$ cm in \[{\text{c}}{{\text{m}}^2}\] is:

Answer Verified Verified
Hint: Congruent circles are circles that have the same size, that is they have the same radii, same circumference and same area. We can calculate the area of the circle using the formula,$A = \pi {R^2}$, where $R$ is the radius of the circle. Then, the area of the congruent circle will also be the same.

Complete step-by-step answer:
Congruent circles are circles that have the same size, that is they have the same radii, same circumference and the same area.
Congruent circles completely overlap each other.
Area of the circle is the space enclosed by the circle.
Area of the circle is given by the formula, $A = \pi {R^2}$, where $R$ is the radius of the circle .
On substituting the value of given radius as $r$ cm, we get
$
  A = \pi {R^2} \\
  A = \pi {r^2} \\
$
Now, we have to find the area of the congruent circle.
As, congruent circle will also have the same area.
Hence, the area of the congruent circle will also be $\pi {r^2}$\[{\text{c}}{{\text{m}}^2}\].
Thus, the area of two congruent circles is $\pi {r^2}{\text{ c}}{{\text{m}}^2}$.

Note:- The congruent figures have the same shape and size. The congruent circles have the same area. Also, the formula used in the calculation of area of circle is $A = \pi {R^2}$, where $R$ is the radius of the circle . Mention the unit of area after calculating the area of congruent circles.

Bookmark added to your notes.
View Notes
×