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
A rectangular plot of land measures 45 m x 30 m. A boundary wall of height 2.4 m is built all around the plot at a distance of 1 m from the plot. Find the area of the inner surface of the boundary wall.
The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If the area of the rectangle is three times the area of the square; find the dimensions of each.
Calculate the area of quadrilateral ABCD, in which ∠ABD = 90°, triangle BCD is an equilateral triangle of side 24 cm and AD = 26 cm.
Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm ∠A = 90° and BC = CD = 52 cm.
The figure given below shows the cross-section of a concrete structure. Calculate the area of cross-section if AB = 1.8 cm, CD = 0.6 m, DE = 0.8 m, EF = 0.3 m and AF = 1.2 m.
Find the area and perimeter of a square plot of land, the length of whose diagonal is 15 meters. Given your answer correct to 2 places of decimals.
Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.
| Vertices | Area (sq.units) |
| (0, 0), (p, 8), (6, 2) | 20 |
Find the area of the quadrilateral whose vertices are at (– 9, 0), (– 8, 6), (– 1, – 2) 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)
If vertices of a quadrilateral are at A(– 5, 7), B(– 4, k), C(– 1, – 6) and D(4, 5) and its area is 72 sq. units. Find the value of k.
