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
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.
Find the area of a triangle formed by the lines 3x + y – 2 = 0, 5x + 2y – 3 = 0 and 2x – y – 3 = 0
Find the area of the unshaded region
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
Find the area of a parallelogram given in figure. Also find the length of the altitude from vertex A on the side DC.
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.
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.
A design is made on a rectangular tile of dimensions 50 cm × 70 cm as shown in the following figure. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile.
