Question

The perimeter of a square is $40$ cm. How do you find its area?

Answer 1

Start by mentioning the definition of perimeter of a square. Then we will mention the formula for the perimeter of square and substitute values in the formula. Then finally evaluate the conditions and solve for the dimensions of the square and area of the square.

Complete step by step answer:
First we will start off by mentioning the definition of perimeter. So, perimeter is a path that surrounds a two-dimensional shape. This term may be used either for the path, or its length in one dimension.
Now, the perimeter of a square is given by, $4a$.
Now substitute values in the formula and solve for the value of the side of the square that is $a$.
$\,\,P = 4a \\\ 40 = 4a \\\ \,\,a = 10 \\\$
Hence, the length of the side of the square is $10$cm.
Now we will evaluate the area of the square.
Area of square is given by ${a^2}$.
Now, we will substitute values in the formula and solve for the area of the square.
$A = {a^2} \\\ A = 10 \times 10 \\\ A = 100\,c{m^2} \\\$
Hence, the area of the square is $100\,c{m^2}$.
Additional information:
A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as the rectangle in which two adjacent sides have equal length. A square is a special case of rhombus which has equal sides, opposite equal angles.

Note: While mentioning the definition, make sure to mention the terms properly. Reduce the terms by factorisation. While choosing any variable, for any unknown term, choose according to the conditions.