Calculate the perimeter and area of a rectangle with sides of 6 dm and 4 dm and a square with a side of 5 dm.
Calculate the perimeter and area of a rectangle with sides of 6 dm and 4 dm and a square with a side of 5 dm. Compare the perimeters of these shapes and then their areas.
Take a rectangle ABCD with length a and width b:
| AB | = | CD | = a;
| BC | = | AD | = b;
The side of the square KLMN is denoted by c:
| KL | = | LM | = | MN | = | KN | = c
By the condition of the problem:
a = 6 dm;
b = 4 dm;
c = 5 dm;
The task requires:
calculate the perimeter and area of the rectangle ABCD;
calculate the perimeter and area of the square KLMN;
find out which of the found areas and perimeters is larger.
Area and Perimeter Formulas
To calculate the perimeter of an arbitrary rectangle, including a square, it is necessary to add the lengths of all four sides. To calculate the area of an arbitrary rectangle, including a square, it is necessary to multiply the length by the width. We get:
The perimeter of rectangle ABCD is: P1 = | AB | + | BC | + | CD | + | AD | = 2 * a + 2 * b;
The perimeter of the square KLMN is: P2 = | KL | + | LM | + | MN | + | KN | = 4 * c;
The area of the rectangle ABCD is: S1 = | AB | * | BC | = | CD | * | AD | = a * b;
The area of the square KLMN is: S2 = | AB | * | BC | = | CD | * | AD | = c * 2;
To solve the problem, let’s substitute the initial data here and compare the obtained values.
Calculating and comparing areas and perimeters
The perimeter and area of the rectangle ABCD are:
P1 = 2 * a + 2 * b = 2 * 6 + 2 * 4 = 20 (dm);
S1 = a * b = 6 * = 24 (dm²);
The perimeter and area of the KLMN rectangle are:
P2 = 4 * c = 4 * 5 = 20 (dm);
S2 = c * 2 = 5 * 2 = 25 (dm²);
Comparing the results obtained, we get the answer:
the perimeters of the rectangle and the square are the same and equal to 20 dm², and the area of the square is 25 dm² larger than the area of the rectangle of 24 dm².
