The adjacent sides of parallelogram are 26cm and 28cm and one of its diagonal is 30cm. Find the area of parallelogram by using heron's formula
well, you have a triangle whose area is half that of the parallelogram. Use Heron's formula on it, since you have all three sides. Then double the result.
672cm square
To find the area of a parallelogram using Heron's formula, we first need to find the lengths of the other diagonal.
Let's label the sides of the parallelogram:
Let's say the adjacent sides are a = 26 cm and b = 28 cm, and the diagonal is c = 30 cm.
In a parallelogram, the diagonals bisect each other. Therefore, the other diagonal (d) is equal to half the length of the other diagonal formed by the two adjacent sides (c).
So, d = c/2 = 30 cm/2 = 15 cm.
Now, we have all the side lengths of the parallelogram. According to Heron's formula, the area of a parallelogram can be found by using the formula:
Area = √(s(s-a)(s-b)(s-c)),
where s is the semi-perimeter of the parallelogram, given by the formula:
s = (a + b + c + d)/2.
Let's plug in the values:
s = (26 cm + 28 cm + 30 cm + 15 cm)/2 = 99 cm/2 = 49.5 cm.
Now, we can calculate the area using Heron's formula:
Area = √(49.5 cm(49.5 cm - 26 cm)(49.5 cm - 28 cm)(49.5 cm - 30 cm)).
Simplifying further:
Area = √(49.5 cm(23.5 cm)(21.5 cm)(19.5 cm)).
Finally, we can calculate the area:
Area = √(49.5 cm * 23.5 cm * 21.5 cm * 19.5 cm).
Using a calculator, you can find the value of the expression inside the square root and get the final area of the parallelogram.