Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let a be the length of each side of the rhombus.
4a = perimeter
4a = 52
a = 13 cm
(i) It is given that,
AC= 24 cm
We have to find BD.
Now
`a^2 = ( "AC"/2 )^2 + ( "BD"/2)^2`
`13^2 = 12^2 + ("BD"/2)^2`
`( "BD"/2 )^2 = 5^2`
BD = 10 cm
Hence the other diagonal is 10cm.
(ii) Area of the rhombus = `1/2` x AC x BD
= `1/2` x 24 x 10
= 120 sq.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.
A rectangular plot of land measures 45 m x 30 m. A boundary wall of height 2.4 m is built all around the plot at a distance of 1 m from the plot. Find the area of the inner surface of the boundary wall.
The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If the area of the rectangle is three times the area of the square; find the dimensions of each.
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 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 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.
Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.
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.
Find the area of quadrilateral PQRS.
If the diagonal d of a quadrilateral is doubled and the heights h1 and h2 falling on d are halved, then the area of quadrilateral is ______.
