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

**Problem 723**

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

**Problem 723**

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

**Square**

Area, $A = a^2$

Perimeter, $P = 4a$

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

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**Problem 24**

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

**Problem 01**

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

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.

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**Problem 53**

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

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**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.

**Problem 21**

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

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