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.
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
Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
A rectangular plot 85 m long and 60 m broad is to be covered with grass leaving 5 m all around. Find the area to be laid with grass.
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.
Calculate the area of the figure given below: which is not drawn scale.
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 diagram, given below, shows two paths drawn inside a rectangular field 80 m long and 45 m wide. The widths of the two paths are 8 m and 15 m as shown. Find the area of the shaded portion.
A floor that measures 15 m x 8 m is to be laid with tiles measuring 50 cm x 25 cm. Find the number of tiles required.
Further, if a carpet is laid on the floor so that a space of 1 m exists between its edges and the edges of the floor, what fraction of the floor is left uncovered?
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.
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.
