## Perimeter of the curve r = 4(1 + sin theta) by integration

**Problem**

What is the perimeter of the curve *r* = 4(1 + sin θ)?

A. 32

B. 30

C. 34

D. 28

**Problem**

What is the perimeter of the curve *r* = 4(1 + sin θ)?

A. 32

B. 30

C. 34

D. 28

**Situation**

A swimming pool is shaped from two intersecting circles 9 m in radius with their centers 9 m apart.

Part 1: What is the area common to the two circles?

A. 85.2 m^{2}

B. 63.7 m^{2}

C. 128.7 m^{2}

D. 99.5 m^{2}

Part 2: What is the total water surface area?

A. 409.4 m^{2}

B. 524.3 m^{2}

C. 387.3 m^{2}

D. 427.5 m^{2}

Part 3: What is the perimeter of the pool, in meters?

A. 63.5 m

B. 75.4 m

C. 82.4 m

D. 96.3 m

**Quadrilateral** is a polygon of four sides and four vertices. It is also called *tetragon* and *quadrangle*. For triangles, 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.

The following formulas are applicable only to convex quadrilaterals.

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