Question

Find the area of figure obtained by joining the midpoints of adjacent sides of a rectangle of sides 8cm and 6cm

Answer 1

$\huge{Hey\:Mate\:Here\: Is\: Your\: Answer}$

$\textbf{Given That....}$

We Need To Find Area Of Of Figure Obtained by joining Mid-point Of Adjacent Sides Of Rectangle Having

Sides 8cm & 6cm.

$\underline{Giving\:Answer \:In \:Attachment..}$

$\textbf{Hence The Required Answer Is...}$

$\boxed{ar(PQRS) \: = \: 24 {cm}^{2} }$

Answer 2

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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