In a rectangle of length =8cm and breadth = 6 cm, if the midpoints of all its four sides are joined then which figure is formed. Also find its area.
Answers
breadth=b=6cm
if midpoints of all four sides of rectangle are joined the figure formed is Rhombus
area of the rhombus= d1d2/2
= (8*6)/2
=24 cm^2 here d1= diagonal=length of the rectangle
d2= breadth of the rectangle
Given : 8 सेमी और 6 सेमी की आसन्न भुजाओं वाले आयत के मध्य बिन्दुओं को मिलाने से बनने वाली आकृति
A rectangle of sides 8 cm & 6 cm . Figure formed join mid points of rectangle
To Find : आकृति कौन सी है , क्षेत्रफल
Formed Figure and area
Solution:
क्षेत्रफल 24 सेमी² वाला समचतुर्भुज
विकर्ण 1 = 8 सेमी
विकर्ण 2 = 6 सेमी
विकर्ण एक-दूसरे के लंबवत
=> समचतुर्भुज
क्षेत्रफल = (1/2) x विकर्ण 1 x विकर्ण 2
= (1/2) x 8 x 6
= 24 सेमी²
As mid points are joined
Hence Diagonals are parallel to rectangle sides and equal to them
Diagonals are 8 cm & 6 cm in length
and perpendicular to Each other
Hence figure formed is Rhombus
Area = (1/2)* 8 * 6 = 24 cm²
Another method : Area of rectangle = 6 x 8 = 48 cm²
Triangle removed from corners are right angle with sides 8/2 = 4 cm and sides 6/2 = 3 cm
area of each triangle = (1/2) * 4 * 3 = 6
area of 4 triangles = 4 x 6 = 24 cm²
Area of figure formed = 48 - 24 = 24 cm²
Side length = √3² + 4² = 5
A rhombus with side = 5 cm
क्षेत्रफल 24 सेमी² वाला समचतुर्भुज
Rhombus of area 24 cm²
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