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
Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
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 area of a rectangular is 640 m2. Taking its length as x cm; find in terms of x, the width of the rectangle. If the perimeter of the rectangle is 104 m; find its dimensions.
How many tiles, each of area 400 cm2, will be needed to pave a footpath which is 2 m wide and surrounds a grass plot 25 m long and 13 m wide?
The perimeter of a rhombus is 52 cm. If one diagonal is 24 cm; find:
(i) The length of its other diagonal,
(ii) Its area.
Using the information in the following figure, find its area.
In the following, find the value of ‘a’ for which the given points are collinear
(2, 3), (4, a) and (6, – 3)
Find the area of the quadrilateral whose vertices are at (– 9, – 2), (– 8, – 4), (2, 2) and (1, – 3)
Let P(11, 7), Q(13.5, 4) and R(9.5, 4) be the midpoints of the sides AB, BC and AC respectively of ∆ABC. Find the coordinates of the vertices A, B and C. Hence find the area of ∆ABC and compare this with area of ∆PQR.
Find the area of quadrilateral BCEG
