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
A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes ?
The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied
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
Using Heron’s formula, find the area of a triangle whose sides are 10 cm, 24 cm, 26 cm
An advertisement board is in the form of an isosceles triangle with perimeter 36 m and each of the equal sides are 13 m. Find the cost of painting it at ₹ 17.50 per square metre.
The area of the isosceles triangle is `5/4 sqrt(11)` cm2, if the perimeter is 11 cm and the base is 5 cm.
The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.
In the following figure, ∆ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ∆ABC is constructed. Find the height DF of the parallelogram.
