   Chapter 8.2, Problem 50E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Prove that the area of a square whose diagonal has length d is A =   1 2 d 2 .

To determine

To Prove:

Area of a square whose diagonal has length d is A= 12d2.

Explanation

Proof:

Let’s consider a square ABCD with side length 's' and diagonal length 'd'.

The square is a special case or type of both the rectangle and the rhombus. The properties of square concern its sides, angles and diagonals.

1. Opposite sides are parallel.

2. All sides are congruent.

3. All angles are right angles.

4. Diagonals are equal.

5. Diagonals are perpendicular bisector of each other.

The theorem on quadrilateral with perpendicular diagonals says that the area A of any quadrilateral with perpendicular diagonals of lengths d1 and d2 is given by A=12d1d2

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