Advertisements
Advertisements
प्रश्न
Two adjacent sides of a parallelogram are 34 cm and 20 cm. If one of its diagonal is 42 cm, find: area of the parallelogram.
उत्तर
At first we have to calculate the area of the triangle having sides 34cm, 20cm and 42cm.
Now,
s = `(34 + 20 + 42)/(2)`
= 48cm
∴ Area of triangle
= `sqrt(48(48 - 34)(48 - 20)(48 - 42)`
= `sqrt(48 xx 14 xx 28 xx 6)`
= `sqrt(4 xx 12 xx 2 xx 7 xx 4 xx 7 xx 2 xx 3)`
= `sqrt(4 xx 4 xx 2 xx 2 xx 7 xx 7 xx 36)`
= 4 x 2 x 7 x 6
= 336cm2
∴ Area of parallelogram
= 2 x Area of triangle
= 2 x 336
= 672cm2.
APPEARS IN
संबंधित प्रश्न
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Show that the diagonals of a square are equal and bisect each other at right angles.
Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure). Show that
- It bisects ∠C also,
- ABCD is a rhombus
State, 'true' or 'false'
The diagonals of a parallelogram bisect each other at right angle.
State, 'true' or 'false'
Each diagonal of a rhombus bisects it.
State, 'true' or 'false'
If the diagonals of a quadrilateral bisect each other at right angle, the quadrilateral is a square.
In the given figure ABCD is a rhombus with angle A = 67°
If DEC is an equilateral triangle, calculate:
- ∠CBE
- ∠DBE
In a square ABCD, diagonals meet at O. P is a point on BC such that OB = BP.
Show that:
- ∠POC = `[ 22 ( 1°)/( 2 ) ]`
- ∠BDC = 2 ∠POC
- ∠BOP = 3 ∠CPO
PQRS is a rectangle in which PQ = 12cm and PS = 8cm. Calculate the area of ΔPRS.
The area of a floor of a rectangular room is 360m2. If its length is 24cm, find its perimeter.
A rectangular floor 45 in long and 12 m broad is to be paved exactly with square tiles, of side 60 cm. Find the total number of tiles required to pave it.
If a carpet is laid on the floor such as a space of 50 cm exists between its edges and the edges of the floor, find what fraction of the floor is uncovered.
A rectangular hall of 40m by 24m is covered with carpets of size 6m x 4m. Find the number of carpets required to cover the hall.
The area of a rhombus is 234 cm2. If its one diagonal is 18 cm, find the lengths of its side and the other diagonal. Also, find perimeter of the rhombus.
A rectangular field is 240m long and 180m broad. In one corner a farm house is built on a square plot of side 40m. Find the area of the remaining portion and the cost of fencing the open sides Rs.25per m.
The diagonals of a square are perpendicular to one another.
All the sides of a rhombus are of equal length.
The opposite sides of a trapezium are parallel.
Examine whether the following is a polygon. If it is not, say why?
Examine whether the following is a polygon. If it is not, say why?
