# Square

## Common Quadrilaterals

**Square**

Perimeter, $P = 4a$

Diagonal, $d = a\sqrt{2}$

## 01 Area enclosed by line rays inside a square

**Problem**

The figure shown below is a square of side 4 inches. Line rays are drawn from each corner of the square to the midpoints of the opposite sides. Find the area of the shaded region.

## 10 Area common to three squares inside the regular hexagon

**Problem**

Three squares are drawn so that each will contain a side of regular hexagon as shown in the given figure. If the hexagon has a perimeter of 60 in., compute the area of the region common to the three squares. The required area is the shaded region in the figure.

## The Quadrilateral

Quadrilateral is a polygon of four sides and four vertices. It is also called tetragon and quadrangle. In the triangle, the sum of the interior angles is 180°; for quadrilaterals the sum of the interior angles is always equal to 360°

**Classifications of Quadrilaterals**

There are two broad classifications of quadrilaterals; *simple* and *complex*. The sides of simple quadrilaterals do not cross each other while two sides of complex quadrilaterals cross each other.

Simple quadrilaterals are further classified into two: *convex* and *concave*. Convex if none of the sides pass through the quadrilateral when prolonged while concave if the prolongation of any one side will pass inside the quadrilateral.

## 21 - 24 Solved problems in maxima and minima

**Problem 21**

Find the rectangle of maximum perimeter inscribed in a given circle.