the measures of a pair of two adjacent sides of a parallelogram are 15cm and 20 cm.if the length of one of its diagonal is 25cm, find the area of the parallelogram
The parallelogram has sides 15cm 20cm 15cm 20cm
The diagonal of length 25cm divide it into two congruent triangles
Using the heron formula to find the area of a triangle and multiplying by two we get the area of parallelgram
Triangle with sides 15cm 20 cm 25 cm
Putting the values in heron formula we get
sqrt(s(s-a)(s-b)(s-c))
= sqrt(30 * 15*10*5)
= 15*2*5
= 150
Area of parallelogram =150 *2
= 300
The figure is a rectangle, since
15^2 + 20^2 = 25^2
The area is thus 15*20 = 300
To find the area of the parallelogram, we first need to find the length of the other diagonal, as both diagonals of a parallelogram bisect each other and create four congruent right triangles.
Let's label the sides of the parallelogram as follows:
AB = 15 cm (one side)
BC = 20 cm (adjacent side)
AC = diagonal (25 cm)
Using the Pythagorean theorem, we can find the length of the other diagonal (BD):
BD^2 = AB^2 + AD^2
Since the diagonals bisect each other, AD is half the length of the diagonal AC. Thus, AD = AC/2.
Substituting the values, we get:
BD^2 = 15^2 + (25/2)^2
BD^2 = 225 + 625/4
BD^2 = 900/4 + 625/4
BD^2 = 1525/4
BD = √(1525/4) ≈ 19.56 cm
Now that we have the lengths of both diagonals (AC = 25 cm and BD ≈ 19.56 cm), we can calculate the area of the parallelogram using the formula:
Area = (1/2) * AC * BD
Substituting the values:
Area = (1/2) * 25 cm * 19.56 cm
Area ≈ 244.5 cm^2
Therefore, the area of the parallelogram is approximately 244.5 square centimeters.