Determine the area of two regular shapes from given data?
1. An office 9.3m long and 7.6m wide is to be carpeted so as to leave a surround 500mm wide. Calculate the area of the carpet 2. Find the area of a trapezium whose parallel sides are 7m and 9m long and whose altitude is 5m 3. An isosceles triangle had a base 118mm long and the two equal sides are each 143mm long. Calculate the area of the triangle. 4. Find the area of a circle whose diameter is 28m Mathematics for Engineering Technicians
Given mean and standard deviation, can you determine if it is bell shaped?
It is possible to derive the mean and standard deviation for any data set of one variable, whether it conforms well to a bell shape or not. So the shape of the curve cannot be found from the mean and standard deviation. What shape would I expect? There are only 50 data, and it is quite possible that no two have the same value. That would flatten the curve. Using grouped data it might conform well to the bell shape, but that is only a guess, and should not be passed off as analysis.
Given that the sides of an irregular polygon are 6cm, 8cm, 10cm, and 12cm respectively, how can the angles and diagonals be calculated?
Fixing the four sides of a quadrilateral won't determine it's shape. One would need either one of the diagonals or one of the interior angles to do that. But even given those, there still may be some ambiguity unless the order of the sides is specified.To see that at least 5 numbers are needed, realize that 4 veticies require 8 numbers. But one vertex can be fixed at the origin and another on the x or y axis. This leaves 5 independent numbers to determine the quadrilateral.
Using z-score to determine mean and standard deviation?
Because it is population data (and not sample data), we can in fact solve for the population mean and standard deviation. We know that the equation z = (X-µ)/σ holds true, so writing out 2 equations from the given data above, we get -2 = (40-µ)/σ --> -2σ = 40-µ and 3 = (90-µ)/σ --> 3σ = 90-µ Then we can treat σ and µ as the variables X and Y and solve using systems of equations. ♠
How can I find the area of an irregular quadrilateral if I only know the length of all four sides and the two diagonal lengths?
In your figure, take two triangles ABC and ADC.Use the formula for area of triangle to find the two ares, and then add to get total area.Formula for area of triangle in terms of sides a,b,c:Semi-perimeter [math] s=(a+b+c)/2 [/math]Area [math] A= \sqrt{(s(s-a)(s-b)(s-c))} [/math]Here both diagonals are within the area, so we add the areas. If "diagonal" AC were outside the area, in which case, DB will be short, then we have to subtract the areas.
I have the four sides of an irregular quadrilateral and none of its angles. How can I calculate its area?
Brahmagupta (c.598 - 665) was an Indian mathematician who gave his formula for finding the area of a quadrilateral, which does not require the angle measurements. Only the 4 lengths are sufficient to find the area. We should give him due credit!Brahmagupta's FormulaBrahmagupta's formula finds the area of a cyclic quadrilateral. The formula for the area of a cyclic quadrilateral with sides a, b, c, d is given bywhere s = [a+b+c+d]/2and a, b, c and d are the four sides.Example 1: Let ABCD be a kite. DA = AB = 3, DC = CB = 5. Let us find the area of the kite.s = (3+3+4+4)/2 = 14/2 = 7Area = [(7–3)(7–4)(7–4)(7–3)]^0.5 = (4x3x4x3)^0.5 = 12.As you can see DAC is a RAT as also ABC, with AC as the hypotenuse (5). Therefore area of DAC and ABC = 3*4/2 = 6 each, and so area of ABCD = area DAC + area ABC = 6+6 = 12, same as what we got from Brahmagupta’s formula.Example 2: Let PQRS be a kite. SP = PQ = 5, QR = RS = 12. Let us find the area of the kite.s = (5+5+12+12)/2 = 34/2 = 17Area = [(17–5)(17–12)(17–12)(17–5)]^0.5 = (12x5x5x12)^0.5 = 60.As you can see SPR is a RAT as also PQR, with PR as the hypotenuse (13). Therefore area of SPR and PQR = 5*12/2 = 30 each, and so area of PQRS =area SPR + area PQR = 30 + 30 = 2*30 = 60, same as what we got from Brahmagupta’s formula.
How do you find the area of shapes in sectors?
I have to find the area of the shaded region but I have no idea how to do it! Please help and explain it because my teacher sucks at explaining!!!(in case you can't tell in the picture, the shaded area Is the circle.)
How do I know if any two given polygons intersect/overlap?
1. First find if there's an intersection between the edges of the two polygons.2. If not, then choose any one point of the first polygon and test whether it is fully inside the second.3. If not, then choose any one point of the second polygon and test whether it is fully inside the first.4. If not, then you can conclude that the two polygons are completely outside each other.For #1, use bounding boxes to shortlist the regions to be tested. If the polygons are really huge, some kind of spatial hierarchy trees could be used too.