# rectangle

## 723 Rectangle, quarter circle and triangle | Centroid of Composite Area

## Common Quadrilaterals

**Square**

Perimeter, $P = 4a$

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

## 24-25 Largest rectangle inscribed in a circular quadrant

**Problem 24**

Find the area of the largest rectangle that can be cut from a circular quadrant as in Fig. 76.

## 01 Rectangle of maximum perimeter inscribed in a circle

**Problem 01**

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

## 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.

## 53 - 55 Solved Problems in Maxima and Minima

**Problem 53**

Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.

## 32 - 34 Maxima and minima problems of a rectangle inscribed in a triangle

**Problem 32**

Find the dimension of the largest rectangular building that can be placed on a right-triangular lot, facing one of the perpendicular sides.

## 21 - 24 Solved problems in maxima and minima

**Problem 21**

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