Chapter 11.1, Problem 33WE

To determine

To Derive: The area of triangle using the area of rectangle.

Answer to Problem 33WE

  $\frac{1}{2}bh$

Explanation of Solution

Given:

  

  

We know that the diagonal of the rectangle divide the rectangle in two parts having equal areas.

Thus

  $\begin{array}{l}{A}_1=A_2\mathrm{...}(i)\\ A_3=A_4\mathrm{...}(ii)\end{array}$

Area of rectangle

  $\begin{array}{l}A=A_1+A_2+A_3+A_4\\ bh=2(A_1+A_3)\\ A_1+A_3=\frac{1}{2}bh\end{array}$

Hence, the area of the triangle is $\frac{1}{2}bh$