Find the area of a rhombus if its vertices ar | vedclass

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(B) Let the vertices of the rhombus $ABCD$ be $A(3,0), B(4,5), C(-1,4)$ and $D(-2,-1)$.The area of a rhombus is given by the formula $	ext{Area} = \f

Vedclass · Accepted Answer

$24$

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(B) Let the vertices of the rhombus $ABCD$ be $A(3,0), B(4,5), C(-1,4)$ and $D(-2,-1)$.The area of a rhombus is given by the formula $	ext{Area} = \frac{1}{2} 	imes d_1 	imes d_2$,where $d_1$ and $d_2$ are the lengths of the diagonals.First,calculate the length of diagonal $AC$ using the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$:$AC = \sqrt{(-1-3)^2 + (4-0)^2} = \sqrt{(-4)^2 + 4^2} = \sqrt{16+16} = \sqrt{32} = 4\sqrt{2}$.Next,calculate the length of diagonal $BD$:$BD = \sqrt{(-2-4)^2 + (-1-5)^2} = \sqrt{(-6)^2 + (-6)^2} = \sqrt{36+36} = \sqrt{72} = 6\sqrt{2}$.Now,calculate the area:$	ext{Area} = \frac{1}{2} 	imes AC 	imes BD = \frac{1}{2} 	imes 4\sqrt{2} 	imes 6\sqrt{2} = \frac{1}{2} 	imes 24 	imes 2 = 24$ square units.

Find the area of a rhombus if its vertices are $(3,0), (4,5), (-1,4)$ and $(-2,-1)$ taken in order. (in square units)

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