Question

Derive a formula for the area of the triangle shown by using the formula for the area of a rectangle.

Short answer

The area of triangle is$A=\frac{1}{2}bh$ .

Step-by-step solution

Step 1. Given information.

Given a figure,

Step 2. Concept  Used.

The area of the rectangle is
$A=bh$

Step 3. Let’s derive the formula of area of triangle using the area of rectangle.

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

Thus,

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

Area of rectangle

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

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