0
Still curious? Ask our experts.
Chat with our AI personalities
Judy
Taiga
SteveAdd your answer:
Earn +20 pts
Find the perimeter and area of a rectangle with width 3 meters and length 11 meters?
Oh, what a happy little rectangle we have here! To find the perimeter, we add up all the sides, which would be 2 times the width plus 2 times the length. So, 2(3) + 2(11) = 6 + 22 = 28 meters for the perimeter. And to find the area, we simply multiply the width by the length, which gives us 3 x 11 = 33 square meters of area. Just remember, there are no mistakes, only happy little accidents!
How do you prove the formula for the area of a triangle?
Easiest wayDraw a three inch by three inch square. add lines at one inch marks to form a small grid. draw line diagonally across to form two triangles. count the number of squares in one triangle (remember the squares with the diagonal line are only half a square)Did you get 4 1/2?A X B divided by two 3 X 3= 9 / 2 = 4.5To arrive to the forumla for area of triangle, lets look at the area of square and rectanlge first: Area of square: side x side Area of rectangle: length x width Notice that the formulas for area of square and rectangle is very similar. The squre is a special case only, so there is not much difference. Let's take the special case first- area of square: Area= side x side If I want to find the area of a triangle from this square, you have to divide the square in half diagonally. This means: (side x side)/2 = area of triangle Let's take a look at retangle now: Area of rectangle: length x width Similarly like the square, you divide the rectangle diagonally by half. This means: (length x width)/2 Conclusion: Thus, area of triangle= (base x height)/2 The base can be considered as one of the sides of the rectangle/square, and the height can be considered as the other side of the rectangle/square. THE FORMULA OF TRIANGLE COMES FROM HALF THE AREA OF RECTANGLE/SQUARE! Visit quickanswerz.com for more math help and tutoring!Area is measured in square units. If we are given a region we divide the region into unit squares.Then we count the number squares, which is the area of the region.Consider a rectangle of length 10 units and width 5 units.The area of the rectangle is 50 square units.It is because we can divide the rectangle into 10 equal parts along the length.Similarly, we can divide the rectangle into 5 equal parts along the width. Now we have divided the entire rectangle into unit squares.If we count the number of squares we get 50 unit squares.We get this by multiplying the length and the width. Area = Length*Width square units.This is the same for a parallelogram too.Area of a parallelogram is base * height square unitsThis is how the concept of area has come.We can find the area of the triangle also.A rectangle or a parallelogram can be divided into two equal triangles by a diagonal.Half of the area of the rectangle(or parallelogram) gives the area of the triangle.In fact, we can extend any triangle into an parallelogram.So, we get the formula, area of a triangle = (base* height)/2 square units.Source: www.icoachmath.com
How do you calculate the top dimensions of a rectangle if you know its perimeter and bottom area?
Important to note are these formulae: Perimeter_of_rectangle = 2 x (length + width) Area_of_rectangle = length x width So if the perimeter and area are known, then: 2 x (length + width) = perimeter => length + width = perimeter / 2 => length = perimeter / 2 - width length x width = area => (perimeter / 2 - width) x width = area (substituting for length given above) => perimeter / 2 x width - width2 = area => width2 - perimeter / 2 x width + area = 0 which is a quadratic and can be solved either by factorization or by using the formula: width = (perimeter / 2 +/- sqrt(perimeter2 / 4 - 4 x area)) / 2 = (perimeter +/- sqrt(perimeter2 - 16 x area)) / 4 This will provide two values for the width. However, each of these values is the length for the other, so the larger value is the length and the smaller value is the width. Sometimes only 1 value will be found for the width above. In this case, the rectangle is actually a square which means that the length and width are both the same. Examples: 1. perimeter = 6, area = 2 width2 - perimeter / 2 x width + area = 0 => width2 - 6 / 2 x width + 2 = 0 => width2 - 3 x width + 2 = 0 => (width - 2) x (width - 1) = 0 => width = 2 or 1. So the length is 2 and the width is 1. 2. perimeter = 12, area = 9 width2 - perimeter / 2 x width + area = 0 => width2 - 12 / 2 x width + 9 = 0 => width2 - 6 x width + 9 = 0 => (width - 3)2 = 0 => width = 3 So the rectangle is a square with both length and width of 3.
The width of a rectangle is 6 inches less than twice the length find the dimension of the rectangle if its area is 108 square inches?
Let the length of the rectangle be L and the width W, then W = 2L - 6 The area of a rectangle = L x W : 108 = L x (2L - 6) = 2L2 - 6L. Expressing this as a standard quadratic equation gives : 2L2 - 6L - 108 = 0. This can be factored as (2L + 12)(L - 9) = 0. As we are only concerned with positive solutions then the negative solution can be ignored, thus, When L - 9 = 0 then L = 9. As L = 9 then W = 2L - 6 = 18 - 6 = 12. The dimensions of the rectangle are : Width 12 inches, Length 9 inches.
How do you find volume when width and height is given?
Volume is a 3 dimensional attribute . Not only do you have to know the width and the height but also the length. If the width is, say, the diameter of a cylinder than you can easily find the area of the cross section (pi * r2) and multiply that by the height to get the volume.
