Advertisements
Advertisements
प्रश्न
Find the value of k, if the area of a quadrilateral is 28 sq. units, whose vertices are (– 4, – 2), (– 3, k), (3, – 2) and (2, 3)
Advertisements
उत्तर
Let the vertices A(– 4, – 2), B(– 3, k), C(3, – 2) and D(2, 3)
Area of the Quadrilateral = 28 sq. units
`1/2[(x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1) - (x_2y_1 + x_3y_2 + x_4y_3 + x_1y_4)]` = 28
`1/2[(-4"k" + 6 + 9 - 4) - (6 + 3"k" - 4 - 12)]` = 28
`1/2[(-4"k" + 11) - (3"k" - 10)]` = 28
– 4k + 11 – 3k + 10 = 56
– 7k + 21 = 56
– 7k = 56 – 21
– 7k = 35
⇒ 7k = – 35
k = `35/7`
= – 5
The value of k = – 5
APPEARS IN
संबंधित प्रश्न
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
A rectangular plot 85 m long and 60 m broad is to be covered with grass leaving 5 m all around. Find the area to be laid with grass.
The cost of enclosing a rectangular garden with a fence all around, at the rate of 75 paise per metre, is Rs. 300. If the length of the garden is 120 metres, find the area of the field in square metres.
The length of a rectangular verandah is 3 m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x as the breadth of the verandah, write an equation in x that represents the above statement
(ii) Solve the equation obtained in (i) above and hence find the dimensions of the verandah.
Two adjacent sides of a parallelogram are 28 cm and 26 cm. If one diagonal of it is 30 cm long; find the area of the parallelogram. Also, find the distance between its shorter sides.
The shaded region of the given diagram represents the lawn in the form of a house. On the three sides of the lawn, there are flowerbeds having a uniform width of 2 m.
(i) Find the length and the breadth of the lawn.
(ii) Hence, or otherwise, find the area of the flower-beds.
A triangle and a parallelogram have the same base and the same area. If the side of the triangle is 26 cm, 28 cm, and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
The floor of a room is of size 6 m x 5 m. Find the cost of covering the floor of the room with 50 cm wide carpet at the rate of Rs.24.50 per metre. Also, find the cost of carpeting the same hall if the carpet, 60 cm, wide, is at the rate of Rs.26 per metre.
Find the diagonal of a quadrilateral whose area is 756cm2 and the perpendicular from the opposite vertices are 17cm and 19cm.
Find the area of quadrilateral BCEG
