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

Problem 723
Locate the centroid of the shaded area in Fig. P-723.

Common Quadrilaterals




Area, $A = a^2$

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°

$A + B + C + D = 360^\circ$


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.

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