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For understanding this complex problem, let's do it in two parts. First we will find the dimensions of the rectangle and based on that we can find the area of a triangle inscribed in it.Using the equation of ellipse and differential calculus, mathematical formula for the area of a rectangle is, area = 2ab, where 2a = major axis and 2b = minor axis.The largest triangle that can be inscribed in the rectangle, should stand on the same base & has height raising between the same parallel sides of the rectangle.The area of largest triangle inscribed within the rectangle is ... Read More
A regular decagon is a ten sided polygon with all sides and angles equal. And here we need to find the area of a decagon that is inscribed inside a circle using the radius of the circle r, Mathematical formula for the side of the decagon inscribed in the circle, a = r√(2-2cos36o)(Using cosine rules)Formula for finding area of decagon, Area = 5*a2*(√5+2√5)/2 Area = 5 *(r√(2-2cos36))^2*(√5+2√5)/2 Area = (5r2*(3-√5)*(√5+2√5))/4Using this formula in a program, Example#include #include int main() { float r = 8; float area = (5 * pow(r, 2) * (3 - sqrt(5))* (sqrt(5) ... Read More
A Hexagon is a closed figure of 6 side and a regular hexagon is the one which has all six sides equal and angle equal. For finding the area of hexagon, we are given only the length of its diagonal i.e d.The interior angles of Hexagon are of 120 degrees each and the sum of all angles of a Hexagon is 720 degrees.The formula to find the area of hexagon with side length a, Area = (3a2 √3) / 2.Since all sides are of same size and angle is 120 degrees, d = 2a or a = d/2By putting the ... Read More
An n-sided regular polygon inscribed in a circle, the radius of this circle is given by the formula, r = a/(2*tan(180/n))Suppose a polygon have 6 faces i.e., a hexagon and as we know mathematically that the angle is 30 degreeSo the radius of circle will be (a / (2*tan(30)))Therefore, r = a√3/2We see the polygon can be divided into N equal triangles. Looking into one of the triangles, we see that the whole angle at the center can be divided into = 360/NSo, angle x = 180/n Now, tan(x) = (a / 2) * r So, r = a / ... Read More
To find the area of a circle inside a right angled triangle, we have the formula to find the radius of the right angled triangle, r = ( P + B – H ) / 2.Given the P, B and H are the perpendicular, base and hypotenuse respectively of a right angled triangle.Area of a circle is given by the formula, Area = π*r2where π = 22 / 7 or 3.14 and r is the radius of the circle.Hence the area of the incircle will be given by the formula, Area = π* ((P + B – H) / 2)2.Example#include ... Read More
PL/SQL stands for “Procedural Language extension to SQL” . It is the mixture of SQL and Procedural features provided by programming language. It was developed by Oracle Corporation in the late 1980s as procedural extension language for SQL and the Oracle relational database.PL/SQL programs consists of blocks that can be nested and a block structure look likes this −DECLARE -- it contains declaration statements BEGIN -- It contains executable statements EXCEPTIONS -- It contains exception handling statements END;ExampleIn PL/SQL single-line comments begin with double hyphen(--) and Multi-line comments begin with a slash-asterisk ( /* ) and end ... Read More
Javascript has provided the getAttributeNode() method to find the attribute node with the specified name of an element, as an attribute object. If the attribute does not exist, the return value is null or an empty string ("").syntaxelement.getAttributeNode(attributename);It returns the attribute object representing the specified attribute node ExampleIn the following example, there are two heading tags with different classes. Those tags when accessed by the getAttributeNode() can return the attribute class with which they attached. It works the same as an array. We can access the multiple classes only by providing their index numbers.Live Demo Tutorix Tutorialspoint var elmnt ... Read More
The HTML DOM embed object is associated with the HTML element.The element can be used to embed various external applications like audio, video etc.PropertiesFollowing are the properties for the HTML DOM embed object −PropertyDescriptionHeightTo set or return the embed element height attribute value.SrcTo set or return the src attribute value in an embedded element.TypeTo set or return the type attribute value in an embed element.WidthTo set or return the width attribute value in an embed element.SyntaxFollowing is the syntax for −Creating an embed object −var e = document.createElement("EMBED");ExampleLet us look at an example for the embed object − ... Read More
Whenever you make a method final, you cannot override it. i.e. you cannot provide implementation to the superclass’s final method from the subclass.i.e. The purpose of making a method final is to prevent modification of a method from outside (child class).Still, if you try to override a final method a compile time error is generated.Exampleinterface Person{ void dsplay(); } class Employee implements Person{ public final void dsplay() { System.out.println("This is display method of the Employee class"); } } class Lecturer extends Employee{ public void dsplay() { System.out.println("This is display method of ... Read More
The HTML DOM console.warn() method is used to display a warning message in the console. In some browsers there is a small exclamation mark in console log for these warnings The console.warn() method will not interrupt your code execution. Developers can use the console.warn() method to give warnings to the user about some user action.SyntaxFollowing is the syntax for console.warn() method −console.warn(message)Here, the message is a mandatory parameter of type string or object. It is displayed as a warning in the console view.ExampleLet us look at an example for the console.warn() method − console.warn() Method Click the below ... Read More