Chapter 11.1, Problem 12PSB

To determine

To find : The area and perimeter of the square MNOP

Answer to Problem 12PSB

The area is $32$ square units and the perimeter is $16\sqrt{2}$ units

Explanation of Solution

Given information : The following information has been given

Area of square ABCD is $64$ square units

MNOP are midpoints of sides of ABCD

Formula used : The area of any square will be

  $A={(lengt{h}_1)}^2$

Calculation : We know that as MNOP are midpoints of sides of ABCD, the area of MNOP will be half of ABCD. Hence, we have

  $A=\frac{1}{2}(64)=32$ square units

Now, as we know that $A=32$ , hence for each side of the square MNOP, we can say that

  $a=\sqrt{32}=4\sqrt{2}$ units

Thus, the perimeter is

  $P=4a=4(4\sqrt{2})=16\sqrt{2}$