Rectangle width 4 m length 12 cm, find the area of a rectangle with the same perimeter.

univerkov | May 5, 2021 | education

The width of the rectangle (apr.) – 4 cm;

The length of the rectangle (bpr.) – 12 cm;

Square area Sq. -? cm ^ 2.

Perimeter of the rectangle (Ppr.) = (Pkv.)

The perimeter of the rectangle is found according to the formula:

Ppr. = (apr. + bpr.) * 2.

We substitute the known values into this formula and find the value of the perimeter of the rectangle:

Ppr. = (4 + 12) * 2 = 16 * 2 = 32 (cm).

The perimeter of the square is found by the formula: Pkv. = 4 * aq.

By condition, the perimeter of the rectangle is equal to the perimeter of the square, i.e. 4 * aq. = 32, therefore, the side of the square is equal to aq. = 32: 4 = 8 cm.

The area of the square is calculated by the formula:

Sq. = (aq.) ^ 2 = 8 ^ 2 = 64 (cm ^ 2).

Answer: the area of the square is 64 cm ^ 2.

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