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A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Find the area of the parallelogram.

Solution:

Given, the field is in the form of parallelogram

The sides are 60 m and 40 m

One of its diagonals is 80 m

Consider a parallelogram ABCD

AB = CD = 60 m

BC = AD = 40 m

BD = 80 m

We know that area of parallelogram ABCD = 2 (area of triangle BCD)

In triangle BCD,

a = 60 m

b = 40 m

c = 80 m

Area of triangle = √s(s - a)(s - b)(s - c)

Where s = semiperimeter

s = (a + b + c)/2

So, s = (60 + 40 + 80)/2

= 180/2

s = 90 cm

Area = √90(90 - 60)(90 - 40)(90 - 80)

= √90(30)(50)(10)

= √100 × 5 × 100 × 27

= 100√9 × 3 × 5

= 300√15 cm²

Area of triangle BCD = 300√15 cm²

Area of parallelogram ABCD = 2(300√15)

= 600√15

Therefore, area of parallelogram is 600√15 cm²

✦ Try This: A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12

NCERT Exemplar Class 9 Maths Exercise 12.3 Problem 6

Summary:

A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. The area of the parallelogram is 600√15 cm²

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