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#Quadrilateral shapes geometry equations how to#

Trapezium: The bases of the trapezium are parallel to each other.A rhombus is a parallelogram whose diagonals are perpendicular to each other. The diagonals are perpendicular to and bisect each other. Length of Diagonal = Length Area= (length) 2 A square is a special type of parallelogram whose all sides and angles are equal. Opposite sides are parallel to each other. Squares: All sides and angles are congruent.A rectangle is a special type of parallelogram whose angles are right. Opposite angles formed at the point where diagonals meet are congruent. The diagonals are congruent and bisect each other. Rectangle: Opposite sides are parallel and congruent.If one of the angles of a parallelogram is right angle then all other angles are a right angle and the parallelogram becomes a rectangle.Īrea = Length X Height Perimeter = 2X (length + breadth) Diagonals bisect each other and each diagonal divide the parallelogram into two congruent triangles. Parallelogram: Opposite sides are parallel and congruent.Therefore, the sum of interior angles= 3 X 360°= 1080°Īgain, we have sum of interior angles = (n-2) X 180°, where n is the number of sides of the polygon. We know that in a regular polygon sum of all the exterior angles is 360° SOLUTION: Sum of interior angles of a regular polygon is 3 times the sum of exterior angles. Determine the number of sides of the polygon. We know that, exterior angle + interior adjacent angle = 180° So, if the polygon has n sides, then Sum of all exterior angle + Sum of all interior angle = n X 180° So, sum of all exterior angle= n X 180° - sum of all interior angle = n X 180° - (n-2) X 180° = n X 180° - (n X 180°) +(2 X 180°) = 360° Each Exterior Angle= 360°/n Number of sides of a polygon= 360°/(each exterior angle)ĮXAMPLE 1: The exterior angles of a quadrilateral are (m+1) °, (2m+3) °, (4m+5) °, (5m +6) °.

#Quadrilateral shapes geometry equations how to#

We will learn now how to find the sum of exterior angles of a polygon having n sides. Sum of the measure of exterior angle of polygon

Apothem: A line from the centre of a regular polygon at a right angle to any of its Area of a regular polygon= perimeter X apothem/2 The interior angle and the exterior angle add up to 180 degrees. Each Exterior Angle= 360°/N Interior Angle: Angle formed by two adjacent sides inside the polygon. Exterior Angle: The exterior angle is the angle between any side of a shape, and a line extended from the next side. Diagonal: A line connecting two vertices that isn’t a side.

\Polygon Parts: Side: One of the line segments that make up the polygon.

Sum of interior angles of a polygon= (N-2) X 180 degrees Number of diagonals in a polygon= ½ X N X (N-3) Number of triangles in a polygon= (N-2) where N is the no.

At least one interior angle is more than 180 degrees. Concave Polygon: We can draw at least one straight line through a concave polygon that crosses more than two sides. Every interior angle is less than 180 degrees. Convex Polygon: A straight line drawn through a convex polygon crosses at most two sides. Regular polygons are both equiangular and equilateral. Types of Polygons: Regular Polygon: All angles are equal and all sides are the same length.

A polygon can be defined as a geometric object consisting of a number of points and an equal number of line segments.

A quadrilateral has 4 edges (sides) and 4 vertices (corners).

A quadrilateral is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on.

Do not despair, though, because a few of them yield to area formulas, just as the square does.

$quadrilateral shapes geometry equations$

They are symmetrical, but are not required to have congruent sides or angles. What is an irregular quadrilateral? Irregular quadrilaterals are: rectangle, trapezoid, parallelogram, kite, and rhombus. You can easily see that a rectangle may have four 90° interior angles, but it need not have four equal-length sides. Regular polygons have congruent sides and angles. Of the long list, only a square is a regular quadrilateral.