( Geometry Math Sheet shapes @ solids(ملخص لقوانين الاشكال الهندسية والمجسمات مع وسيلة ايضاح)

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Geometry Math Sheet shapes @ solids(ملخص لقوانين الاشكال الهندسية والمجسمات مع وسيلة ايضاح)







Square



A square is a four sided regular polygon. The circumference of a square with sides of length s is:





The area of a square is:






Rectangle



The rectangle is a 4 sided polygon, quadrilateral, with right angle
corners. The circumference of a rectangle with side lengths of x and y
is:





The area of a rectangle is:






Circle



The circle is a shape where all points along the shape are equal
distance from a specific point. This point is the center of the circle
and the distance to the center of the circle is the radius. The
circumference of a circle of radius r is:





The area of a circle is:






Triangle



The triangle is a 3 sided polygon. Triangles can be classified by their sides:

1. Equilateral triangles: All sides are equal in length.
   
2. Isosceles triangles: Two sides are equal in length.
   
3. Scalene triangles: All sides have different lengths.
   

Triangles can also be classified by their angles:

1. Right triangle: One angle is 90 degrees.
   
2. Oblique triangle: Has no angle equal to 90 degrees.
   
3. Obtuse triangle: One angle is greater than 90 degrees.
   
4. Acute triangle: All angles are less than 90 degrees.
   

The circumference of a triangle is the sum of all sides of the triangle.





The area of a triangle is determined by its base and height.






Parallelogram



A parallelogram is a 4 sided polygon or quadrilateral with two sets
of parallel sides. The opposite sides are equal in length. The
circumference of a parallelogram is:





The area of a parallelogram is:






Circular Sector



The circular sector is section of a circle enclosed by two radii. The
length of the arc of a circular sector, where r is the radii and theta
is the angle, is:





The area of the circular sector is:






Circular Ring



The circular ring or donut shape is composed of a circle with a
centered small circle removed from the area. The area of a circular
ring, where R is the outer diameter and r is the inner diameter, is:






Trapezoid



A trapezoid is a 4 sided polygon or quadrilateral with one set of parallel sides. The circumference of the trapezoid is:





The area of a trapezoid is:






Sphere



The sphere is a 3 dimensional object, whose surface is continuous and
all points of the surface are an equal distance from a fixed point, the
center. The surface area of a sphere, where r is the radius, is:





The volume of a sphere is:






Cube



A cube is a three dimensional object bounded by 6 equal square sides.
The surface area of a cube , where the length of a side is l, is:





The volume of a cube is:






Rectangular Box



A rectangular box is a three dimensional object bounded by
rectangular or square sides. The surface area of a rectangular box,
where the lengths of the sides are a, b, c, is:





The volume of a rectangular box is:






Cylinder



The cylinder, also know as the right circular cylinder, is formed by
rotating a line, of length h, around a fixed axis parallel to that line.
A cylinder has two ends that are equally sized circles parallel to one
another and the circular side is at a right angle to these circular
ends. The surface area of cylinder is:





The volume of a cylinder is:






Right Circular Cone



The right circular cone is a three dimensional object created by
rotating a right triangle about the vertical side. The surface area of a
right circular cone is:





Where the slant height, s is:





The volume of a right circular cone is:






Frustum of a Cone



The frustum of a cone is a portion of cone with the top removed. The
top and bottom surfaces are parallel to one another. The volume of a
frustum of a cone, where the top radius is r and the bottom radius is R,
is:






Pythagorean Theorem



The Pythagorean theorem is based upon the right triangle. And If the
three sides of the right triangle are a,b, and c, where c is the
hypotenuse, the formula is:

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