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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q33. (page 427)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

Given a figure,

02

Step 2. Concept Used.

The area of the rectangle is
$A = b h$

03

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,

$\begin{array}{l} A_{1} = A_{2} ... (i) \\ A_{3} = A_{4} ... (i i) \end{array}$

Area of rectangle

$\begin{array}{l} A = A_{1} + A_{2} + A_{3} + A_{4} \\ b h = 2 (A_{1} + A_{3}) \\ A_{1} + A_{3} = \frac{1}{2} b h \end{array}$

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

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