Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let ABCD be a parallelogram field with sides AB = CD = 60 m, BC = DA = 40 m and diagonal BD = 80 m.
Area of parallelogram ABCD = 2(Area of ΔABD) ...(i)
In ΔABD,
Semi-perimeter of a triangle ΔABD,
`s = (a + b + c)/2`
= `(AB + BD + DA)/2`
= `(60 + 80 + 40)/2`
= `180/2`
= 90 m
∴ Area of ΔABD = `sqrt(s(s - a)(s - b)(s - c))` ...[By Heron’s formula]
= `sqrt(90(90 - 60)(90 - 80)(90 - 40))`
= `sqrt(90 xx 30 xx 10 xx 50)`
= `100 xx 3sqrt(15)`
= `300sqrt(15) m^2`
From equation (i),
Area of parallelogram ABCD = `2 xx 300sqrt(15) = 600sqrt(15) m^2`
Hence, the area of the parallelogram is `600sqrt(15) m^2`.
APPEARS IN
RELATED QUESTIONS
Find the area of a triangle whose base and altitude are 5 cm and 4 cm respectively.
Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.
Determine whether the sets of points are collinear?
`(-1/2, 3), (-5, 6) and (-8, 8)`
Find the area of triangle AGF
A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y-axis. The path travelled by the man is
Find the area of a triangle formed by the lines 3x + y – 2 = 0, 5x + 2y – 3 = 0 and 2x – y – 3 = 0
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m2 a year. A company hired one of its walls for 6 months. How much rent did it pay?
The perimeter of a triangular field is 420 m and its sides are in the ratio 6 : 7 : 8. Find the area of the triangular field.
How much paper of each shade is needed to make a kite given in the following figure, in which ABCD is a square with diagonal 44 cm.
A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1 m2 of the field, find the total cost of ploughing the field.
