Advertisements
Advertisements
प्रश्न
If the diagonal d of a quadrilateral is doubled and the heights h1 and h2 falling on d are halved, then the area of quadrilateral is ______.
Advertisements
उत्तर
If the diagonal d of a quadrilateral is doubled and the heights h1 and h2 falling on d are halved, then the area of quadrilateral is `underlinebb(1/2(h_1 + h_2)d)`.
Explanation:
Let ABCD be a quadrilateral, where h1 and h2 are altitudes on the diagonal BD = d.
Then, area of quadrilateral `ABCD = 1/2(h_1 + h_2) xx BD`
If altitudes are halved and the diagonal is doubled, then
Area of quadrilateral `ABCD = 1/2(h_1/2 + h_2/2) xx 2d`
= `1/2((h_1 + h_2)/2) xx 2d`
= `1/2(h_1 + h_2) xx d`
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.
The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.
Find the area of a quadrilateral one of whose diagonals is 30 cm long and the perpendiculars from the other two vertices are 19 cm and 11 cm respectively.
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.
A floor that measures 15 m x 8 m is to be laid with tiles measuring 50 cm x 25 cm. Find the number of tiles required.
Further, if a carpet is laid on the floor so that a space of 1 m exists between its edges and the edges of the floor, what fraction of the floor is left uncovered?
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.
In the following, find the value of ‘a’ for which the given points are collinear
(2, 3), (4, a) and (6, – 3)
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)
Find the area of quadrilateral BCEG
