Advertisements
Advertisements
प्रश्न
A triangle and a parallelogram have the same base and the same area. If the side of the triangle is 26 cm, 28 cm, and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Advertisements
उत्तर
Let the sides of the triangle be
a = 26 cm, b = 28 cm and c = 30 cm
Now,
semi-perimeter of a triangle,
s = `( a + b + c )/( 2 ) = ( 26 + 28 + 30 )/(2 )= (84)/(2) = 42 cm`
∴ Area of triangle = `sqrt (s( s - a )( s - b )(s -c ))`
= `sqrt (42( 42 - 26 ) ( 42 - 28 ) (42 - 30 ))`
= `sqrt ( 42 xx 16 xx 14 xx 12 )`
= `sqrt( 7 xx 6 xx 4 xx 4 xx 7 xx 2 xx 6 xx 2)`
= `sqrt( 7 xx 7 xx 4 xx 4 xx 6 xx 6xx 2xx 2)`
= 7 x 4 x 6 x 2
= 336 cm2
Base of a parallelogram = 28 cm
Given ,
Area of parallelogram = Area of triangle
⇒ Base x Height = 336
⇒ 28 x Height = 336
⇒ Height = 12 cm
APPEARS IN
संबंधित प्रश्न
The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.
The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles; find the area of the quadrilateral.
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.
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.
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.
The area of a rhombus is 216 sq. cm. If it's one diagonal is 24 cm; find:
(i) Length of its other diagonal,
(ii) Length of its side,
(iii) The perimeter of the rhombus.
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.
Find the area and the perimeter of a square with diagonal 24 cm. [Take √2 = 1.41 ]
Find the area of quadrilateral BCEG
