Chapter 14.6, Problem 4PSA

To determine

To construct the triangle with the same area as given square.

Explanation of Solution

Given:

The square $ABCD$ .

Calculation:

Let the area of given square ABCD be $a^2$ whose side is $a$ unit.

Now, the construction of triangle ABC having the area equal to the above square is as follows-

Here,

  $\begin{array}{l}BC=2a\\ AB=a\end{array}$

  

The area of triangle ABC is equal to $\frac{1}{2}\times a\times 2a=a^2$