Chapter 4.2, Problem 55STP

To determine

To Calculate:

The area of smaller square.

Answer to Problem 55STP

  $128c{m}^2$

Explanation of Solution

Given Information:

The midpoints of the sides of the large square are joined to form a smaller square.

  

Concept Used:

PYTHAGORAS THEOREM/ PYTHAGOREAN THEOREM :

It is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of areas of the squares on the other two sides.

  $a^2+b^2=c^2$

where

a = side of the right angled triangle

b = side of the right angled triangle

c = hypotenuse

Calculation:

Let the length of a side of the smaller square be represented by s .

So, the formula for area of the square would be $A=s^2$ .

Use the Pythagorean theorem to find the length of a side of the smaller square.

  $\begin{array}{l}{a}^2+b^2=s^2\mathrm{...........................}[Pythagorean\_theorem]\\ \Rightarrow 8^2+8^2=s^2\mathrm{.......................}[a=b=\frac{16}{2}\mathrm{.....}midpo\mathrm{int}]\\ \Rightarrow 64+64=s^2\mathrm{......................}[simplify]\\ \Rightarrow 128=s^2\mathrm{............................}[simplify]\end{array}$

So,

  $\begin{array}{l}\sin ce\\ A=s^2\\ \Rightarrow A=128c{m}^2\end{array}$

Hence,the correct answer is B.