Question

A tabletop is covered with 25 squares of equal sizes. The side of the square is 3 cm. The area of the tabletop is
(A) 300 sq. cm
(B) 225 cm
(C) 225 sq. cm
(D) 300 cm

Answer 1

Hint: The side of the square is 3 cm. We know the formula, \[\text{Area=}{{\left( \text{side} \right)}^{2}}\] . Use this formula and get the area of the square. As the tabletop is covered with 25 squares of equal sizes, the area of each square is equal to \[9\,c{{m}^{2}}\] . Now, calculate the area of 25 squares. Since the top of the table is covered with 25 squares, the area of the top of the table is equal to the summation of the area of 25 squares. Solve it further and get the area of the tabletop.

Complete step-by-step answer:

According to the question, it is given that the tabletop is covered with 25 squares of equal sizes.
The side of the square = 3 cm ……………………………(1)
We know the formula, \[\text{Area=}{{\left( \text{side} \right)}^{2}}\] ……………………(2)
Now, using the formula shown in equation (2), we can calculate the area of the square.
Putting the value of the side of the square from equation (1) in equation (2), we get
\[\text{Area=}{{\left( 3\,cm \right)}^{2}}=9\,c{{m}^{2}}\] ……………………….(3)
As the tabletop is covered with 25 squares of equal sizes, the area of each square is equal to \[9\,c{{m}^{2}}\] .
Area of 25 squares = \[25\times 9\,c{{m}^{2}}=225\,c{{m}^{2}}\] ………………..(4)
Since the top of the table is covered with 25 squares, the area of the top of the table is equal to the summation of the area of 25 squares.
Area of the top of the table = Area of 25 squares …………………(5)
From equation (4), we have an area of 25 squares.
Now, putting the value of the area of 25 squares from equation (4) in equation (5), we get
 Area of the top of the table = \[225\,c{{m}^{2}}\] .
Therefore, the area of the top of the table is \[225\,c{{m}^{2}}\] .
Hence, the correct option is (C).

Note: As the value of the area of the top of the table is 225 so, one might go with the option (B). This is wrong. Since the side of the square is given in centimeters, so the unit of the area of the square should be in \[c{{m}^{2}}\] . But here, in option (B) the area is in centimeters and centimeters can never be the unit of the area.