Question

The area of rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order is
a. 24 sq. units
b. 23 sq. units
c. 25 sq. units
d. 22 sq. units

ALIGARH MUSLIM UNIVERSITY +2 ENTRANCE TEST PAPER 2013-14

Answer 1

Let the given points are A(3,00,B(4,5),C(-1,4) and D(-2,-1) of a rhombus ABCD.

Length of diagonal AC :

$\sqrt{3 - (-1)^2 + (0-4)^2}$

$\sqrt{(16 + 16)}$

$\sqrt{32}$

$4 \sqrt{2}$



Lenth of diagonal BD;

$\sqrt{4 - (-2)^2 + (5 - (-1))^2}$

$\sqrt{36 + 36}$

$\sqrt{72}$

$6 \sqrt{2}$


We know that Area of rhombus = 1/2 * (AC * BD)

                                                      $= \frac{1}{2} * 4\sqrt{2} * 6 \sqrt{2}$

                                                    = 24 sq.units.



Hope this helps!

Answer 2

Length of diagonal AC :

3 - (-1)^2 + (0-4)^2}√​3−(−1)​2​​+(0−4)​2​​​​​ 

√ { (16 + 16)}√​(16+16)​​​ 

√{32}√​32​​​ 

4 \√ { 2}4√​2​​​ 



Lenth of diagonal BD;

√{4 - (-2)^2 + (5 - (-1))^2}√​4−(−2)​2​​+(5−(−1))​2​​​​​ 

\√{36 + 36}√​36+36​​​ 

\√. {72}√​72​​​ 

6 √\{2}6√​2​​​ 




Area of rhombus = 1/2 * (AC * BD)

                                                      = {1}{2} * 4\√{2} * 6 \√{2}=​2​​1​​∗4√​2​​​∗6√​2​​​ 

                                                    = 24 sq.units.




_________

therefore
.......



The area of rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order is
= 24 sq.units.