Perimeter and Area
Regular Polygons: Characteristics
A REGULAR POLYGON has all its sides and angles equal. ➜ The sum of the interior angles of a polygon is 2n - 4 right angles (n is the number of sides). ➜ The sum of the exterior angles of a convex polygon is 360° .
Rectangles and Squares: Characteristics
Characteristics every RECTANGLE must have are detailed below: ➜ Quadrilateral ➜ Four right angles ➜ Opposite sides must be equal in length and parallel to each other ➜ Diagonals must bisect each other And these are additional characteristics that every SQUARE must possess: ➜ ALL four sides are equal in length ➜ Diagonals must cross at right angles
Circles: Characteristics
Characteristics of a Circle • Perfectly round • Never-ending • Ring • Collection of infinite points • Polygon with an infinite number of sides • Any point on the circle is the same distance from the center • Made up of a closed curved line
Parallelogram: Perimeter Formula
For any parallelogram the following statements are true (see the example attached to this definition for details): ➜ ab = dc ➜ ad = bc The PERIMETER OF A PARALLELOGRAM is therefore determined by the following formula: ▶︎▶︎ P of a parallelogram = 2 (ad + ab) If the length of ad or bc is not given, it can be calculated by using the following formula: ➜ ad = bc = h/cos(∠ecb), where ∠ecb is the angle measured in degree or radian ➜ ∠ecb can be calculated if the length of eb is given: ∠ecb = tan-1(eb/h) Copy and paste the following link into your browser to learn more about working with the formula for the perimeter of a parallelogram: https://www.bing.com/videos/search?q=working+with+the+formula+for+the+perimeter+of+a+parallelogram&&view=detail&mid=9FE347A2DAF9409C67789FE347A2DAF9409C6778&FORM=VRDGAR
Parallelograms: Characteristics
In Euclidean geometry, a PARALLELOGRAM is a (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Triangles: Perimeter Formula
Like any polygon, the PERIMETER OF A TRIANGLE IS the total distance around the outside, which can be found by adding together the length of each side. Or stated as a formula: ➜ Perimeter of a Triangle = a + b + c, where a, b and c are the lengths of each side of the triangle. Copy and paste the following link into your browser to learn more about working with the formula for the perimeter of a triangle: https://www.bing.com/videos/search?q=working+with+the+formula+for+the+perimeter+of+a+triangle&&view=detail&mid=37C51BFC7D5632ECEEB037C51BFC7D5632ECEEB0&FORM=VRDGAR
Trapezoids: Perimeter Formula
Like any polygon, the perimeter of a trapezoid is the total distance around the outside, which can be found by adding together the length of each side. Or as a formula: ➜ Perimeter of a trapezoid = a + b + c + d, where a , b, c, and d are the lengths of each side of the trapezoid. Copy and paste the following link into your browser to learn more about working with the formula for the perimeter of a trapezoid: https://youtu.be/Aavsx1ZZ5V8
Trapezoids: Characteristics
Probably the TRAPEZOID is one of the most popular quadrilaterals when it comes to bridge construction. Numerous railroad trestles and wooden bridges of the nineteenth and early twentieth centuries were trapezoidal in shape. The two parallel sides of a trapezoid are its bases while the legs are the nonparallel sides. The height of a trapezoid is a line segment that runs perpendicular to the bases. The median, or mid-segment, is a line that is parallel to the bases and connects the midpoints of each leg. The area is calculated with a formula using the lengths of each base and the height. A parallelogram is usually defined as a trapezoid, although it has two pairs of parallel sides instead of just one. An isosceles trapezoid has congruent base angles and equal leg lengths.
Triangles: Characteristics
TRIANGLES are one of the basic shapes in the real world. Triangles can be classified by the characteristics of their angles and sides; and triangles can be compared based on these characteristics. The sum of the measures of the interior angles of any triangle is 180º. A TRIANGLE is a polygon with three edges and three vertices. In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane. .
Circle: Area Formula
The AREA OF A CIRCLE is the number of square units [space] inside that circle. If each square in the circle to the left has an area of 1 cm² you could count the total number of squares to get the area of this circle. Thus, if there were a total of 28.26 squares, the area of this circle would be 28.26 cm². However, it is easier to use one of the following formulas: ➜ Area equals Pi [3.14] times r squared OR ➜ Area equals Pi [3.14] times r times r, where 'Area' is the area of a circle, and 'r' is the radius of that specific circle Copy and paste the following link into your browser to learn more about working with the formula for the area of a circle: https://www.bing.com/videos/search?q=working+with+the+formula+for+the+area+of+a+circle&&view=detail&mid=C6A281E13D80143183B4C6A281E13D80143183B4&FORM=VRDGAR
Trapezoids: Area Formula
The AREA OF A TRAPEZOID is represented by the following formula: ➜ Area of a trapezoid = ½ • (b₁ + b₂) • h, where (b₁, b₂) represent the lengths of each base 'h' represents the altitude (height) of the trapezoid. Recall that the bases are the two parallel sides of the trapezoid. The altitude (or height) of a trapezoid is the perpendicular distance between the two bases. Copy and paste the following link into your browser to learn more about working with the formula for the area of a trapezoid: https://www.bing.com/videos/search?q=working+with+the+formula+for+the+area+of+a+trapezoid&&view=detail&mid=7DB4E77AE5B5EEDEBF887DB4E77AE5B5EEDEBF88&FORM=VRDGAR
Triangles: Area Formula
The AREA OF A TRIANGLE is always half the product of the height and base: ➜ Area of Triangle = ½ Base • Height Copy and paste the following link into your browser to learn more about working with the formula for the area of a triangle: https://youtu.be/-IprFDyKPzE
Circle: Circumference [Perimeter] Formula
The distance around a circle is called the CIRCUMFERENCE. The distance across a circle through the center is called the DIAMETER. Pi [3.14 or the symbol '∏'] is the ratio of the of a circle to the diameter. Thus, for any circle, if divide the circumference by the diameter, you get a value close to Pi. Circumference of a circle is expressed in the following formula: ➜ Circumference of a circle = Pi [∏ or 3.14] times the diameter of that specific circle Another way to write this formula is: ➜ Circumference of a circle = 2 times Pi [∏ or 3.14] times the radius of that specific circle Copy and paste the following link into your browser to learn more about working with the formula for the circumference [perimeter] of a circle: https://www.bing.com/videos/search?q=working+with+the+formula+for+the+circumference+%5bperimeter%5d+of+a+circle&&view=detail&mid=32F9A0E3E3636D0A668732F9A0E3E3636D0A6687&FORM=VRDGAR
Rectangles and Squares: Perimeter Formula
The formula for calculating the PERIMETER OF A RECTANGLE OR SQUARE is 2L + 2W, where 'L' is the length of the rectangle / square, and 'W' is the width of that same rectangle / square. For example, if a rectangle has a length of 2 feet and a width of 4 feet, its perimeter equals 12 feet, or 2(4) + 2(2). Copy and paste the following link into your browser to learn more about working with the formula for the perimeter of a rectangle or square: https://youtu.be/itf-xWPuhis
Rectangles and Squares: Area Formula
The formula for the AREA OF A RECTANGLE is length times width, so the area of a rectangle that has a length of 7 centimeters and a width of 3 centimeters is 7 times 3, or 21 square centimeters. The formula for the AREA OF A SQUARE is side squared, so the area of a square that has a side of length of 9 feet is 9 squared, or 81 square feet. Copy and paste the following link into your browser to learn more about working with the formula for the area of a rectangle or square: https://www.bing.com/videos/search?q=working+with+the+formula+for+the+area+of+a+rectangle+or+square&&view=detail&mid=1784E9F696058F1BD2931784E9F696058F1BD293&FORM=VRDGAR
Parallelograms: Area Formula
The length of the base of the parallelogram is equal to the length of the base of the rectangle. The height of that parallelogram is equal to the width (height) of that rectangle. Therefore, the AREA OF THE PARALLELOGRAM is equal to the length of its base times its height. Using variables: ➜ Area = b ∗ h, where b is the length of the base and h is the height of the parallelogram. Copy and paste the following link into your browser to learn more about working with the formula for the area of a parallelogram: https://youtu.be/s8OPoot0IUg
Regular Polygons: Area Formula
To find the AREA OF A REGULAR POLYGON, all you have to do is follow this simple formula: ➜ Area of a regular polygon = 1/2 x perimeter x apothem Here is what that means: ▶︎▶︎ Perimeter is the sum of the lengths of all the sides of the regular polygon ▶︎▶︎ Apothem is a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side. Copy and paste the following link into your browser to learn more about working with the formula for the area of a regular polygon: https://www.bing.com/videos/search?q=working+with+the+formula+for+the+area+of+a+regular+polygon&&view=detail&mid=91806841D0501FFD1CB191806841D0501FFD1CB1&FORM=VRDGAR
Regular Polygons: Perimeter Formula
To find the perimeter of a polygon, take the sum of the length of each side. To find the PERIMETER OF A REGULAR POLYGON, multiply the number of sides by the length of one side. Copy and paste the following link into your browser to learn more about working with the formula for the perimeter of a regular polygon:: https://youtu.be/ydCizxCIvhI
Perimeter, Circumference, Area, Diameter, Pi and Radius: Definitions
▶︎ PERIMETER: The distance around a figure. ▶︎ CIRCUMFERENCE: The distance around a circle. ▶︎ AREA: The number of square units [space] inside a figure or a region. ▶︎ ∏ (Pi): The ratio of the circumference of a circle to its diameter, approximately 3.14. ▶︎ DIAMETER: Straight line through the center of a circle or sphere. ▶︎ RADIUS: Straight line between the center of a circle or sphere to any point on its surface (one half of the diameter).
Perimeter, Circumference, Area, Diameter, Pi and Radius: Formulas
▶︎▶︎▶︎ PERIMETER FORMULAS: ➜ Perimeter for Rectangles: Perimeter = 2l × 2w, where P = perimeter, l = length, and w = width. For example: If a rectangle has a length of 3 and a width of 4, then the perimeter of the rectangle is as follows: (2 x 3) + (2 x 4) = 6 + 8 = 14. ➜ Perimeter for Other Polygons: Simply add the measure of all sides of the polygon. For example: If a triangle's sides measure 3, 6, and 8, then the perimeter is 3 + 6 + 8 = 17. ▶︎▶︎▶︎ CIRCUMFERENCE FORMULA: ➜ Circumference for Circles: Circumference = 2∏r or C= ∏d, where C = circumference, ∏ = pi, r = radius, and d = diameter. For example, if the circle's diameter is 6, its radius is 3. then ∏r = 2 x 3.14 x 3 = 18.84 ▶︎▶︎▶︎ AREA FORMULAS: ➜ Area for Rectangles: Area for Rectangles = l x w, where A = area, l = length, and h = height For example: If a rectangle has a length of 3 and a width of 4, then the area is 3 x 4 = 12. ➜ Area for Parallelograms: Area for Parallelograms, A = bh, where A = area, b = base, and h = height For example: If a parallelogram has a base of 3 and a height of 3, then the area is 3 x 3 = 9. ➜ Area for Triangles: Area for Triangles, A = 1/2 bh, where A = area, b = base, and h = height For example: If a triangle has a base of 4 and a height of 3, then the area is 1/2 (3 x 4) = 1/2 x 12 = 6. ➜ Area for Circles: Area for Circles, A = ∏r² , where A = area, ∏ = pi, and r = radius For example: If a circle has a diameter of 6, then it has a radius of 3. So the area is 3.14 x 32 = 3.14 x 9 = 28.26