Question

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

Answer 1

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

Answer 2

The figure is a rectangle, since

15^2 + 20^2 = 25^2

The area is thus 15*20 = 300

Answer 3

[AI-generated answer — Explain Bot]

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.