ABCD is a parallelogram with side AB=12 cm. Its diagonal AC and BD are of lengths 20 cm and 16 cm respectively. Find the area of parallelogram ABCD.
Avinash Kumar is correct that the formula you used only works for a rhombus. However, Trigonometry isn't strictly needed here. What you need for a parallelogram is the length of one pair of parallel sides, and the perpendicular distance between those two sides. With a side and the diagonals, we can find that.Pardon the blurriness.In this diagram, I've extended side AB to point E, where it intersects the perpendicular that passes through point C. I've also added the perpendicular BF. I've labelled the lengths of the perpendiculars as [math]h[/math], and the lengths of the segments EB and CF as [math]a[/math].Note that each of these makes a useful right triangle. In particular, triangle ACE is a right triangle whose hypotenuse is AC, one of the diagonals we were given: AC = 20. We also know that AB = 12, so AE = [math]12 + a[/math]. Finally, EC = [math]h[/math]. The pythagorean theorem gives us:[math](12 + a)^2 + h^2 = 20^2[/math][math]144 + 24a + a^2 + h^2 = 400[/math][math]a^2 + h^2 + 24a = 256[/math]The other interesting triangle is BDF. This is also a right triangle, and its hypotenuse is BD, the other diagonal we were given: BD = 16. We also know that CD = 12, so DF = [math]12 - a[/math], and of course BF = [math]h[/math]. Again, the pythagorean theorem gives us:[math](12 - a)^2 + h^2 = 16^2[/math][math]144 - 24a + a^2 + h^2 = 256[/math][math]a^2 + h^2 - 24a = 112[/math]Subtracting these two equations gives us:[math]48a = 144[/math][math]a = 3[/math]You can quickly find h as well:[math]h^2 + (12 - 3)^2 = 16^2[/math][math]h^2 + 81 = 256[/math][math]h^2 = 175[/math][math]h = 5 \sqrt {7}[/math]So the area of the parallelogram is just AB times h, or[math]12 * 5 \sqrt {7} = 60 \sqrt {7} [/math](You can see that the area is the base times the height, because if you cut off triangle BCF and moved it over so that BC met with AD, you'd produce a rectangle.)
Two adjacent sides of a parallogram are 24 cm and 18 cm long. If the distance between the longer sides is 12 cm, how do I find the distance between the shorter sides?
Area of a parallogram=base×height………….(1)Area of a parallogram=24×12 sq.cmLet distance between shorter sides=h cmAlso area of parallogram=18×h sq.cm18×h=24×12h=(24×12)/18=16 cm. , Answer
What is the length of other diagonal? Given the adjacent sides of a parallelogram are 30 cm and 20 cm and one of the diagonals is 40 cm.
-A2A-Sketch a paralellogram ABCD. Let AB = CD = 30 cm and BC = AD = 20 cm.One of the diagonals is 40 cm. Let AC = 40 cm.In [math]\triangle ABC[/math], we know all the three sides. Use the cosine rule to find [math]\angle ABC[/math][math]cos(\angle ABC) \ = \frac{AB^2 + BC^2 - AC^2}{2 \cdot AB \cdot AC}[/math]Since the adjacent angles in a parallelogram are supplementary ([math]180^0[/math]), [math]\angle BCD \ = 180^0 - \angle ABC[/math]Now, if you use Cosine rule in [math]\triangle BCD[/math], you can find the length of other diagonal.[math]cos(\angle BCD) \ = \frac{BC^2 + CD^2 - BD^2}{2 \cdot BC \cdot BD}[/math]
The adjacent side of a parallelogram are 15 cm and 10 cm. If the distance between the longer side is 6 cm, what is the distance between the shorter sides?
The area of a parallelogram, A = length of parallel sides* distance between them.Longer sides = 15 cm. Distance between longer sides = 6 cmShorter sides = 10 cm. Distance between shorter sides = ? cmSo area =15*6 = 90 sq cm,So distance between the shorter sides will be 90/10 = 9 cm.
A parallelogram has sides 30 cm and 40 cm. If the distance between the shorter sides is 16 cm, what is the distance between the longer sides?
Area of the parallelogram = Base x HeightTaking base = 30 cm and height = 16 cmArea = 30 x 16 sq cmLet the height between the longer side is h cmSince the area becomes same 40 x h = 30 x 16Height =12 cm
ABCD is a parallelogram. The co-ordinates of A,B, C are (2,3), (-5,2) and (4,1) respectively. Find the co-ordinates of D?
There are three possible co-ordinates of D.To get from A (2,3) to B (-5,2) you need to go 7 to the left and down 1. If you do the same from C (4,1) you get to (-3,0). That is one possible D.To get from B to A you need to go 7 to the right and up 1. If you do the same from C you get to (11,2). That is a second possible D.To get from A to C you need to go 2 to the right and down 2. If you do the same from B you get to (-3,0). You already had that answer.To get from C to A you need to go 2 to the left and up 2. If you do the same from B you get to (-7,4). That is the third possible D.To get from B to C you need to go 9 to the right and down 1. If you do the same from A you get to (11,2). You already had that answer.To get from C to B you need to go 9 to the left and up 1. If you do the same from A you get to (-7,4). You already had that answer.The co-ordinates of D are either (-3,0), (11,2), or (-7,4).
What will the area of a parallelogram be if sides are 8cm and 6cm and one diagonal is 10cm?
twice the area of triangle of sides 6, 8, 10, which is a ratio of 3, 4, 5 triangle whose angles you know.use the angles to find the height of the triangle for the base of your choosing using trig. Area of the triangle is bh/2
Parallelogram diagonal/area..?
Part b first \ Area of a parallelogram is base times height or the product of 2 consecutive sides times the sine of the included angle. so (10)(12) sin (60) =60sqrt(3) = 103.923 Part a use the law of cosines c^2 = a^2 + b^2 - 2abCos(C) c^2 = 10^2 + 12^2 -2(10)(12)Cos(60) c^2 = 100 + 144 -240(.5) c^2 = 124 take sqrt and c = 11.1355 note the to find the other diagonal, conecutive interior angles of a parallelogram add up to 180 degrees so the next angle is 120 degrees. When you use the law of cosines everything is the same except the angle. Cos(120) = -.5 so the other diagonal is sqrt (364) = 19.07878
How do u determine if a quadrilateral is parallel?
The sum of the interior angles of triangle BDC add up to 180 degrees. So (x + `19) + (2x + 6) + (3x + 5) = 180 6x + 30 = 180 x = 25 Let angle ABD have a measure of y degrees. Then y + 93 + 43 = 180 y + 136 = 180 y = 44 degrees measure of angle ABC = measure of angle ABD + measure of angle DBC measure of angle ABC = y + (2x + 6) = 44 + 56 = 100 degrees measure of angle BCD = 3x + 5 = 80 degrees measure of angle ABC + measure of angle BCD = 100 + 80 = 180 degrees This is exactly what we need to say that AB is parallel to CD.
In a parallelogram ABCD, it is given that AB=5 cm, AD=4 cm and BAD=30 cm. What is the area of the parallelogram?
A parallelogram can be divided into two equal triangles ABD and DCB by the diagonal BD.Assuming that