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How do you prove the formula for the area of a rectangle?
The formula for the area of a rectangle is length x breadth. In order to prove this works, work out an area of a rectangle using that formula.
How many sides does an irregular polygon have if it has 252 diagonals showing work?
Let its sides be x and rearrange the diagonal formula into a quadratic equation:- So: 0.5(x^2-3x) = 252 Then: x^2-3n-504 = 0 Solving the quadratic equation: gives x a positive value of 24 Therefore the polygon has 24 sides irrespective of it being irregular or regular
In a regular polygon the ratio of the measure of the exterior angle to the measure of the adjacent interior angle is 4 to 1 how many sides does the polygon have Please show your work?
This is not possible for a normal regular polygon. (A regular polygon has all equal angles and all equal sides. A normal polygon has no intersecting edges.)The smallest regular polygon is an equilateral triangle (a three sided polygon), whose exterior angle measure is twice the measure of its interior angle. A four-sided polygon (a square) has equal interior and exterior angle measures of 90⁰. Starting from a five-sided polygon, the exterior angle measure is smaller than the interior angle measure.Let's assume that the given information is true. So we need to verify it.Let's say that the interior angle of the regular polygon has a measure of x degrees, and the measure of the exterior angle of that polygon is 4x degrees.Since the sum of the interior and the exterior angles of the polygon is 180 degrees (a straight line), the interior angle is 36 degrees.4x + x = 1805x = 1805x/5 = 180/5x = 36The sum of the angles of a polygon = 180⁰(n - 2), where n is the number of the sides of the polygon.The measure of one of the angles of a polygon = 180⁰(n - 2)/n. Substituting the angle measure of 36⁰ into this formula, we have:36⁰ = 180⁰(n - 2)/n (multiply by n to both sides)36⁰n = 180⁰(n - 2)36⁰n = 180⁰n - 360⁰ (add 360⁰ and subtract 36⁰n to both sides)360⁰ = 144⁰n (divide by 144⁰ to both sides)2.5 = n !!That means that a such normal polygon does not exist.
What is the circumference if the area is 379.94 cm square?
The first step is to work out the radius. The formula for area is pi(r2). That equals 379.94, so plug this into the equation and you get a radius of 10.997. The formula for the circumference is pi(2r). Plug the now known radius in and you get 69.097516968554117299881726353374 Therefore the circumference, if the area is 379.94cm2, will be 69.1cm
How do you work out the area of a triangle inside a square?
If you want to figure out just the area of the triangle, the formula is base times height divided by 2. It does not matter if it is inside a square, as long as you have the legnths of all they sides you need to calculate the area of that triangle. If you do not, It would be very difficult.
