Advertisements
Advertisements
प्रश्न
A quadrilateral field of unequal has a longer diagonal with 140m. The perpendiculars from opposite vertives upon this diagonal are 20m and 14m. Find the area of the field.
Advertisements
उत्तर
In quadrilateral ABCD, the sides AB, BC, CD and AD are unequal.
The longer diagonal BD = 140m
AM ⊥ BD, CL ⊥ BD
AM = 20m and CL = 14m.
We split a quadrilateral into triangles and find its area.
We know that,
Area of a Triangle = `(1)/(2)"b.h" "i.e" (1)/(2)("Base" xx "Height")`
Ar(ΔABD) = `(1)/(2)"BD" xx "AL";(Δ"CBD") = (1)/(2)"BD" xx "CM"`
Ar(QuadABCD) = Ar(ΔABD) + Ar(ΔCBD)
= `(1)/(2)"BD" xx "AL" + (1)/(2)"BD" xx "CM"`
= `(1)/(2)"BD" xx ("AL" + "CM")`
= `(1)/(2) xx 140 xx (20 + 14)`
= 70 x 34
= 2380m2.
APPEARS IN
संबंधित प्रश्न
Calculate the area of quadrilateral ABCD, in which ∠ABD = 90°, triangle BCD is an equilateral triangle of side 24 cm and AD = 26 cm.
Trapezium given below; find its area.
The length and the breadth of a rectangle are 6 cm and 4 cm respectively. Find the height of a triangle whose base is 6 cm and the area is 3 times that of the rectangle.
A footpath of uniform width runs all around the outside of a rectangular field 30 m long and 24 m wide. If the path occupies an area of 360 m2, find its width.
The following diagram shows a pentagonal field ABCDE in which the lengths of AF, FG, GH, and HD are 50 m, 40 m, 15 m and 25 m, respectively, and the lengths of perpendiculars BF, CH and EG are 50 m, 25 m and 60 m respectively. Determine the area of the field.
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.
Find the area and the perimeter of a square with diagonal 24 cm. [Take √2 = 1.41 ]
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.
Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.
| Vertices | Area (sq.units) |
| (p, p), (5, 6), (5, –2) | 32 |
In the following, find the value of ‘a’ for which the given points are collinear
(2, 3), (4, a) and (6, – 3)
