The adjacent sides of parallelogram are 26cm and 28cm and one of its diagonal is 30cm. Find the area of the parallelogram by using heron's formula
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To use Heron's formula, we first need to find the lengths of all sides of the parallelogram. Since the adjacent sides of the parallelogram are given, we can divide the parallelogram into two triangles by drawing the diagonal.
Let's consider one of the triangles formed by the diagonal and one of the adjacent sides.
Using the Pythagorean theorem, we can find the length of the other side (base) of this triangle:
(28 cm)^2 = (30 cm)^2 - x^2
x^2 = (30 cm)^2 - (28 cm)^2
x^2 = 900 cm^2 - 784 cm^2
x^2 = 116 cm^2
x = √116 cm
x ≈ 10.77 cm (rounded to two decimal places)
Now, we know the lengths of the base and the height of the triangle, which are 10.77 cm and 26 cm, respectively.
Using Heron's formula, we can calculate the area of the triangle:
s = (10.77 cm + 26 cm + 28 cm) / 2
s = 64.77 cm / 2
s ≈ 32.385 cm
area = √(s(s-10.77 cm)(s-26 cm)(s-28 cm))
area = √(32.385 cm * (32.385 cm - 10.77 cm) * (32.385 cm - 26 cm) * (32.385 cm - 28 cm))
area ≈ √(32.385 cm * 21.614 cm * 6.385 cm * 4.385 cm)
area ≈ √(1905.14 cm^4)
area ≈ 43.66 cm^2 (rounded to two decimal places)
Since the parallelogram has two congruent triangles, the area of the parallelogram is twice the area of one triangle.
Therefore, the area of the parallelogram is approximately 2 * 43.66 cm^2 = 87.32 cm^2 (rounded to two decimal places).