Chapter 11.6, Problem 7P

To determine

To find: the length of each diagonal of a cube.

Answer to Problem 7P

  $A=6.928c{m}^2$ .

Explanation of Solution

Given:

Sides of the cube is 45 cm.

Calculation:

According to the question, all the sides of the triangle is equal, therefore, the triangle is equilateral triangle.

As it is known that the area of the equilateral triangle is $\frac{\sqrt{3}}{4}{a}^2$ .

  

Here, from right triangle ABC, AC is the hypotenuse. Therefore,

By using Pythagoras theorem, $A{C}^2=A{B}^2+B{C}^2$

Thus,

  $\begin{array}{l}A=\frac{\sqrt{3}}{4}{a}^2\\ =\frac{\sqrt{3}}{4}{\left(4cm\right)}^2\left\{\text{substitutes the given value}\right\}\\ =4\sqrt{3}c{m}^2\\ =4\times 1.732\{\text{take}\sqrt{3}=1.732\}\\ =6.928c{m}^2\end{array}$

Hence, the area of the triangle is $A=6.928c{m}^2$ .