Finding the Dimensions of a Square with known Perimeter

Q. If the perimeter of a square is 24 units, then its area is:

1. $18$ sq. units
2. $27$ sq. units
3. $36$ sq. units
4. $45$ sq. units

Q. If the perimeters of two squares are in the ratio $1:3,$ then the ratio of their areas is:

1. $3:1$
2. $1:9$
3. $9:1$
4. $1:3$

Q.

If a wire in the shape of a square is re-bent into a rectangle, then the ____ of both shapes remain same, but _____ may vary.

Q.

Xin used $20\mathrm{yd}$ of fencing to build the walls of a square chicken coop. Which equation and solution represent $x$, the length, in yards, of each wall of the square coop?

Q.

$\square \mathrm{ABCD}$ is a square.$\square \mathrm{PQRS}$ is a square formed by joining the mid-points of $\mathrm{AB},\mathrm{BC},\mathrm{CD},$ and $\mathrm{AD}$respectively $\square \mathrm{EFGH}$is a square formed by joining the mid-points of$\mathrm{PQ},\mathrm{QR},\mathrm{RS}$ and $\mathrm{PS}$ respectively. Find the sum of the perimeters of $\square \mathrm{ABCD},\square \mathrm{PQRS}$ and $\square \mathrm{EFGH}$ if the area of the square$\square \mathrm{EFGH}$ is $25c{m}^2$.

Q.
From the given diagram, calculate the area of the rectangle as shown in the shaded portion.

1. $28{\text{unit}}^2$
2. $35{\text{unit}}^2$
3. $42{\text{unit}}^2$
4. $49{\text{unit}}^2$

Q. A garden is in the shape of square. If its perimeter is $24$ units, then its diagonal length is:

1. $6\sqrt{2}$ units
2. $6$ units
3. $\sqrt{2}$ units
4. $3\sqrt{2}$ units

Q. Jackson runs a total distance of 300 m around a square garden in 5 rounds. Find the side length of the garden.
m

Q. If the perimeter of a square is 20 cm, then:

1. side = 4 cm
2. side = 5 cm
3. area = 16 sq. cm
4. area = 25 sq. cm