ATTENTION! micycle rodriguez,marie christine yaun atong math project summarizon pna n2!!!!! ayaw pud klimti nga magsearch mog inyuha...............para patass!!!!!!!!! RHOMBUS Since a rhombus is a diamond shape whose sides are all the same length, the diagonals are perpendicular to each other. The diagonals cut the rhombus into quarters, where each quarter is a right triangle. The legs of the triangle are 4 and 5 (half of each diagonal), and the hypotenuse is the length of each side of the rhombus. s^2 = 4^2 + 5^2 s^2 = 16 + 25 s^2 = 41 s ~= 6.4 If you dont have a calculator handy, you can tell the only answer that works is 6.4 because the side length has to be bigger than half of either diagonal. 6.4 is the only answer greater than 5 mao na Figure. Diagonals of the rhombus divide it in four congruent right triangles So, the side measure of the rhombus is one fourth of its perimeter, that is 52/4 cm = 13 cm. The measure of the leg of the right triangle is half of the length of the known diagonal, that is 24/2 cm = 12 cm. The measure of another leg is equal to sqrt%2813%5E2-12%5E2%29 = sqrt%28169-144%29 = sqrt%2825%29 = 5 cm in accordance with the Pythagorean theorem. The measure of another diagonal of the rhombus is the doubled length of the leg of the right triangle, that is 2*5 cm = 10 cm. Answer. The second diagonal of the rhombus is 10 cm long. MIC MAO NA akong na search Rhombus Problems Rhombus problems with detailed solutions. Definition of a Rhombus The rhombus is a parallelogram with four congruent sides. A square is a special case of a rhombus. rhombus Properties of a Rhombus These are some of the most important properties of a rhombus. Consider the rhombus ABCD shown in the figure above. 1 - All sides are congruent (equal lengths). length AB = length BC = length CD = length DA = a. 2 - Opposite sides are parallel. AD is parallel to BC and AB is parallel to DC. 3 - The two diagonals are perpendicular. AC is perpendicular to BD. 4 - Opposite internal angles are congruent (equal sizes). internal angle A = internal angle C and internal angle B = internal angle D. 5 - Any two consecutive internal angles are supplementary : they add up to 180 degrees. angle A + angle B = 180 degrees angle B + angle C = 180 degrees angle C + angle D = 180 degrees angle D + angle A = 180 degrees Area of a Rhombus These are three formulas for the area of the rhombus. formula 1: area = a*h , where a is the side length of the rhombus and h is the perpendicular distance between two parallel sides of the rhombus. formula 2: area = a 2*sin (A) = a 2*sin (B). Since angles A and B are supplementary angles, sin (A) = sin (B). formula 3: area = (1/2)*d1*d2, where d1 and d2 are the lengths of the two diagonals. We now present some problems with detailed solutions. Problem 1: The size of the obtuse angle of a rhombus is twice the size of its acute angle. The side length of the rhombus is equal to 10 feet. Find its area. Solution to Problem 1: A rhombus has 2 congruent opposite acute angles and two congruent opposite obtuse angles. One of the properties of a rhombus is that any two internal consecutive angles are supplementary. Let x be the acute angle. The obtuse angle is twice: 2x. Which gives the following equation. x + 2 x = 180 degrees. Solve the above equation for x. 3x = 180 degrees. x = 60 degrees. We use the formula for the area of a triangle that uses the side lengths and any one of the angles then multiply the area by 2. area of rhombus = 2 (1 / 2) (10 feet) 2 sin (60 degrees) = 86.6 feet 2 (rounded to 1 decimal place) Problem 2: The lengths of the diagonals of a rhombus are 20 and 48 meters. Find the perimeter of the rhombus? Solution to Problem 2: Below is shown a rhombus with the given diagonals. Consider the right triangle BOC and apply Pythagoras theorem as follows rhombus problem 2 BC 2 = 10 2 + 24 2 and evaluate BC BC = 26 meters. We now evaluate the perimeter P as follows: P = 4 * 26 = 104 meters. Problem 3: The perimeter of a rhombus is 120 feet and one of its diagonal has a length of 40 feet. Find the area of the rhombus. Solution to Problem 3: A perimeter of 120 when divided by 4 gives the side of the rhombus 30 feet. The length of the side OC of the right triangle is equal to half the diagonal: 20 feet. Let us now consider the right triangle BOC and apply Pythagoras theorem to find the length of side BO. rhombus problem 3 30 2 = BO 2 + 20 2 BO = 10 sqrt(5) feet We now calculate the area of the right triangle BOC and multiply it by 4 to obtain the area of the rhombus. area = 4 ( 1/2) BO * OC = 4 (1/2)10 sqrt (5) * 20 = 400 sqrt(5) feet 2 More references on geometry. https://youtube/watch?v=mZOkpmh_ARw Rhombus Song youtube mic kana nga url e open song sa rhombus A rhombus is actually just a special type of parallelogram. Recall that in a parallelogram each pair of opposite sides are equal in length. With a rhombus, all four sides are the same length.It therefore has all the properties of a parallelogram. See Definition of a parallelogram Its a bit like a square that can lean over and the interior angles need not be 90°. Sometimes called a diamond or lozenge shape. Properties of a rhombus Base Any side can be considered a base. Choose any one you like. If used to calculate the area (see below) the corresponding altitude must be used. In the figure above one of the four possible bases has been chosen. Altitude The altitude of a rhombus is the perpendicular distance from the base to the opposite side (which may have to be extended). In the figure above, the altitude corresponding to the base CD is shown. Area There are several ways to find the area of a rhombus. The most common is (base × altitude). Each is described in Area of a rhombus Perimeter Distance around the rhombus. The sum of its side lengths. See Perimeter of a rhombus Diagonals Each of the two diagonals is the perpendicular bisector of the other. See Diagonals of a rhombus Related polygon topics General Polygon general definition Quadrilateral Regular polygon Irregular polygon Convex polygons Concave polygons Polygon diagonals Polygon triangles Apothem of a regular polygon Polygon center Radius of a regular polygon Incircle of a regular polygon Incenter of a regular polygon Circumcircle of a polygon Parallelogram inscribed in a quadrilateral Types of polygon Square Diagonals of a square Rectangle Diagonals of a rectangle Golden rectangle Parallelogram Rhombus Trapezoid Trapezoid median Trapezium Kite Inscribed (cyclic) quadrilateral Inscribed quadrilateral interior angles Inscribed quadrilateral area Inscribed quadrilateral diagonals Area of various polygon types Regular polygon area Irregular polygon area Rhombus area Kite area Rectangle area Area of a square Trapezoid area Parallelogram area Perimeter of various polygon types Perimeter of a polygon (regular and irregular) Perimeter of a triangle Perimeter of a rectangle Perimeter of a square Perimeter of a parallelogram Perimeter of a rhombus Perimeter of a trapezoid Perimeter of a kite Angles associated with polygons Exterior angles of a polygon Interior angles of a polygon Relationship of interior/exterior angles Polygon central angle Named polygons Tetragon, 4 sides Pentagon, 5 sides Hexagon, 6 sides Heptagon, 7 sides Octagon, 8 sides Nonagon Enneagon, 9 sides Decagon, 10 sides Undecagon, 11 sides Dodecagon, 12 sides MORE ABOUT RHOMBUS Diagonals of a rhombus bisect each other at right angles. Diagonals of a rhombus bisect opposite angles. Area of a rhombus (A) with side length l and perpendicular distance h between opposite sides is given as A = lh VIDEO EXAMPLES: PROPERTIES OF A RHOMBUS EXAMPLE OF RHOMBUS The given figure represents a rhombus. SOLVED EXAMPLE ON RHOMBUS Ques: ABCD is a rhombus. Find the area of ABCD, if AC = 3 in. and BD = 4 in. Choices: A. 9 in.2 B. 6 in.2 C. 7 in.2 D. 8 in.2 Correct Answer: B Solution: Step 1: Area of rhombus = 1/2 � product of diagonals Step 2: AC = 3 in. and BD = 4 in. [Given.] Step 3: Area of ABCD = 1/2 � AC � BD Step 4: = 1/2 � 3 � 4 Step 5: = 12 / 2 = 6 [Substitute AC = 3 and BD = 4.] Step 6: The area of ABCD = 6 in.2. Cool Math Lessons, Games and more! pre-algebra algebra precalc / calc math survival geometry / art puzzles other stuff math lessons math practice math games math dictionary geometry / trig reference Teachers Parents Coolmath 4 Kids Coolified Games Finance Freak Totally Stressed Out Science Monster The Properties of a Rhombus Definitions and formulas for the perimeter of a rhombus, the area of a rhombus, properties of the angles and sides of a rhombus Just scroll down or click on what you want and Ill scroll down for you! perimeter of a rhombus area of a rhombus sides and angles of a rhombus properties of the diagonals of a rhombus properties of the angles of a rhombus POPULAR TOPICS Decimals Properties Factors & Primes Fractions Integers Lines Exponents Functions Factoring Trigonometry The perimeter of a rhombus: To find the perimeter of a rhombus, just add up all the lengths of the sides: Perimeter of a rhombus = x+x+x+x = 4x red line The area of a rhombus: To find the area of a rhombus, multiply the lengths of the two diagonals and divide by 2 (same as multiplying by 1/2): Area of a rhombus = (1/2)ab red line The sides and angles of a rhombus: rhombus The sides of a rhombus are all congruent (the same length.) Opposite angles of a rhombus are congruent (the same size and measure.) Properties of the diagonals of a rhombus: rhombus The intersection of the diagonals of a rhombus form 90 degree (right) angles. This means that they are perpendicular. The diagonals of a rhombus bisect each other. This means that they cut each other in half. red line Properties of the angles of a rhombus: rhombus Adjacent sides (ones next to each other) of a rhombus are supplementary. This means that their measures add up to 180 degrees. x degrees + y degrees = 180 degrees Chat Conversation End
Posted on: Mon, 26 Jan 2015 11:48:08 +0000