Area

If the side of a square is $x$, and its area is $A$, which of the following represents the area if the side is tripled?

The area of a square is $144 \text{ cm}^2$. If its side is increased by $2$ cm, what will be the new area?

Two squares have sides in the ratio $2:3$. What is the ratio of their areas?

A square sheet of side $10$ cm has a small square of side $2$ cm cut out from one corner. What is the area of the remaining sheet?

A rectangular courtyard $20$ m long and $15$ m broad is to be paved with bricks of size $25$ cm by $12$ cm. How many bricks are required?

What is the area of a square whose perimeter is the same as the perimeter of a rectangle with length $12$ cm and breadth $8$ cm?

A square garden has a side of $25$ m. A path of $2$ m width is built inside it along the perimeter. What is the area of the remaining garden?

A picture $40\text{ cm}$ by $30\text{ cm}$ is framed with a wood strip $5\text{ cm}$ wide. Find the area of the wood strip used.

The length of a rectangle is $3\text{ cm}$ more than its breadth. If the perimeter of the rectangle is $34\text{ cm}$, find the area of the rectangle.

A square carpet is laid on a rectangular floor of dimensions $12\text{ m} \times 10\text{ m}$. If the area of the floor not covered by the carpet is $56\text{ m}^2$, find the side of the square carpet.