A hand fan is made by stitching 6 equal size triangular strips of two different types. The dimensions of equal strips are 25cm, 25 cm and 14 cm.Find the area of each type of paper needed to make the hand fan.
To find the area of each type of paper needed to make the hand fan, we can calculate the area of each individual triangular strip and then multiply it by the number of strips used.
First, let's calculate the area of one type of triangular strip. The dimensions of the strip are given as 25 cm, 25 cm, and 14 cm.
To calculate the area of a triangle, you can use Heron's formula, which states that the area of a triangle with sides a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle (s = (a+b+c)/2).
For the given dimensions of the triangle (25 cm, 25 cm, and 14 cm), we can calculate the semi-perimeter s:
s = (25 + 25 + 14) / 2 = 64 / 2 = 32 cm
Now, we can plug in the values into the formula to find the area of one triangular strip:
Area = √(32(32-25)(32-25)(32-14))
Next, we need to determine how many strips of each type are used in making the hand fan. It is mentioned that there are 6 equal-sized triangular strips of two different types. Let's say there are x strips of one type and 6 - x strips of the other type.
Finally, to find the total area of each type of paper needed, we multiply the area of one triangular strip by the number of strips of that type:
Total Area of Type 1 Paper = Area of Type 1 Strip * x
Total Area of Type 2 Paper = Area of Type 2 Strip * (6 - x)
Now, simply substitute the calculated area of one triangular strip and solve for x:
Total Area of Type 1 Paper = Area of Type 1 Strip * x
Total Area of Type 2 Paper = Area of Type 2 Strip * (6 - x)
This will give you the area of each type of paper needed to make the hand fan.