Advertisements
Advertisements
Question
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.
Advertisements
Solution
(i) We know that,
Area of Rhombus = `1/2` x AC x BD
Here
A = 216 sq.cm
AC = 24 cm
BD = ?
Now,
A = `1/2` x AC x BD
216 = `1/2` x 24 x BD
BD = 18 cm.
(ii) Let a be the length of each side of the rhombus.
a2 = `("AC"/2 )^2 + ("BD"/2)^2`
a2 = 122 + 92
a2 = 225
a = 15 cm
(iii) Perimeter of the rhombus = 4a = 60 cm.
APPEARS IN
RELATED QUESTIONS
The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.
The distance between parallel sides of a trapezium is 15 cm and the length of the line segment joining the mid-points of its non-parallel sides is 26 cm. Find the area of the trapezium.
A wire when bent in the form of a square encloses an area = 576 cm2. Find the largest area enclosed by the same wire when bent to form;
(i) an equilateral triangle.
(ii) A rectangle whose adjacent sides differ by 4 cm.
ABCD is a square with each side 12 cm. P is a point on BC such that area of ΔABP: area of trapezium APCD = 1: 5. Find the length of CP.
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.
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.
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.
Using the information in the following figure, find its area.
In the following, find the value of ‘a’ for which the given points are collinear
(2, 3), (4, a) and (6, – 3)
Find the area of quadrilateral BCEG
