Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
At first, we have to calculate the area of the triangle having sides, then its perimeter 28 cm, 26 cm, and 30 cm.
Let a = 28, b = 26, c = 30
S = `[ 28 + 26 + 30 ]/2`
= `84/2`
= 42 cm
By Heron's Formula,
Area of a triangle = `sqrt[s( s - a )( s - b )( s - c )]`
= `sqrt[42( 42 - 28 )( 42 - 26 )( 42 - 30 )]`
= `sqrt( 42 xx 14 xx 16 xx 12)`
= `sqrt( 112896 )`
= 336 cm2
Area of a Parallelogram = 2 × Area of a triangle
= 2 × 336
= 672 cm2
We know that,
Area of a parallelogram = Height × Base
⇒ 672 = Height × 26
⇒ Height = 25.84 cm
∴ The distance between its shorter sides is 25.84 cm.
APPEARS IN
संबंधित प्रश्न
A wire when bent in the form of a square encloses an area of 484 m2. Find the largest area enclosed by the same wire when bent to from:
- An equilateral triangle.
- A rectangle of length 16 m.
Calculate the area of the figure given below:
Which is not drawn scale.
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.
The rate for a 1.20 m wide carpet is Rs. 40 per meter; find the cost of covering a hall 45 m long and 32 m wide with this carpet. Also, find the cost of carpeting the same hall if the carpet, 80 wide, is at Rs. 25. Per meter.
The shaded region of the given diagram represents the lawn in the form of a house. On the three sides of the lawn, there are flowerbeds having a uniform width of 2 m.
(i) Find the length and the breadth of the lawn.
(ii) Hence, or otherwise, find the area of the flower-beds.
Using the information in the following figure, find its area.
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 |
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 |
Find the area of quadrilateral BCEG
When proving that a quadrilateral is a parallelogram by using slopes you must find
