A rectangle has sides of 10 and 12 units.How can the area of a square be computed if it has the same perimeter of the rectangle?
so, what is the perimeter of the rectangle?
The perimeter of a square is 4 times the side s. The area is s^2
Well, if the area of a square is to be computed and it has the same perimeter as the rectangle, then we can start by finding the perimeter of the rectangle. The formula to calculate the perimeter of a rectangle is 2(length + width).
For the given rectangle with sides of 10 and 12 units, the perimeter can be calculated as:
2(10 + 12) = 2(22) = 44 units.
Since the square has the same perimeter, we can compute the length of one side of the square by dividing the perimeter by 4 (since a square has 4 equal sides).
So, the length of one side of the square would be 44/4 = 11 units.
To find the area of the square, we simply square the length of one of its sides. Therefore, the area of the square would be 11 x 11 = 121 square units.
To find the area of a square with the same perimeter as the given rectangle, follow these steps:
Step 1: Calculate the perimeter of the rectangle.
The perimeter of a rectangle is the sum of all its sides. In this case, the rectangle has sides of 10 and 12 units.
Perimeter of rectangle = 2 × (Length + Width) = 2 × (10 + 12) = 2 × 22 = 44 units
Step 2: Find the side length of the square.
Since the square has the same perimeter as the rectangle, the total length of its sides will also be 44 units. As a square has equal sides, divide the perimeter by 4 to find the length of one side.
Side length of the square = Perimeter / 4 = 44 / 4 = 11 units
Step 3: Calculate the area of the square.
The area of a square is found by multiplying the length of one side by itself.
Area of the square = side length × side length = 11 × 11 = 121 square units
Therefore, the area of the square with the same perimeter as the given rectangle is 121 square units.
To find the area of a square when given the perimeter, follow these steps:
1. Find the perimeter of the rectangle: The perimeter is the sum of all sides. For a rectangle with sides of 10 units and 12 units, the perimeter is calculated as P = 2*(length + width). In this case, P = 2*(10 + 12) = 44 units.
2. Determine the side length of the square: Since the square has the same perimeter as the rectangle, the sum of its sides must also equal 44 units. Since a square has all sides equal, divide the perimeter by 4 to get the length of each side. In this case, the side length of the square is 44/4 = 11 units.
3. Calculate the area of the square: The area of a square is determined by squaring the length of its side. So, to find the area, multiply the side length by itself. In this case, the area of the square is 11 * 11 = 121 square units.
Therefore, if a rectangle has sides of 10 units and 12 units, and a square has the same perimeter as that rectangle, the area of the square would be 121 square units.