Question

a large square has an area of 81 square units. another, smaller square has shorter sides. its sides are only one - third as long. what is the area of the smaller square? square units

Explanation:

Step1: Find side - length of large square

Let the side - length of the large square be $s_1$. The area formula for a square is $A = s^2$. Given $A_1=81$ square units, then $s_1=\sqrt{81}=9$ units.

Step2: Find side - length of small square

The side - length of the smaller square $s_2$ is one - third of the side - length of the large square. So $s_2=\frac{1}{3}\times s_1=\frac{1}{3}\times9 = 3$ units.

Step3: Calculate area of small square

Using the area formula $A = s^2$ again, for the smaller square with $s = s_2 = 3$ units, $A_2=s_2^2=3^2 = 9$ square units.

Answer:

9