A plot,in the shape of a quadrilateral XYZW,h | vedclass

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(C) The quadrilateral $XYZW$ is divided into two triangles by the diagonal $XZ$: $	riangle XYZ$ and $	riangle XZW$.For $	riangle XYZ$,the sides are

Vedclass · Accepted Answer

$1014$

Vedclass · Answer

(C) The quadrilateral $XYZW$ is divided into two triangles by the diagonal $XZ$: $	riangle XYZ$ and $	riangle XZW$.For $	riangle XYZ$,the sides are $a = 25 \, m$,$b = 60 \, m$,and $c = 65 \, m$.Semi-perimeter $s_1 = (25 + 60 + 65) / 2 = 150 / 2 = 75 \, m$.Area of $	riangle XYZ = \sqrt{s_1(s_1-a)(s_1-b)(s_1-c)} = \sqrt{75(75-25)(75-60)(75-65)} = \sqrt{75 	imes 50 	imes 15 	imes 10} = \sqrt{562500} = 750 \, m^2$.For $	riangle XZW$,the sides are $a = 65 \, m$,$b = 33 \, m$,and $c = 34 \, m$.Semi-perimeter $s_2 = (65 + 33 + 34) / 2 = 132 / 2 = 66 \, m$.Area of $	riangle XZW = \sqrt{s_2(s_2-a)(s_2-b)(s_2-c)} = \sqrt{66(66-65)(66-33)(66-34)} = \sqrt{66 	imes 1 	imes 33 	imes 32} = \sqrt{69696} = 264 \, m^2$.Total area of the quadrilateral $XYZW = 	ext{Area}(	riangle XYZ) + 	ext{Area}(	riangle XZW) = 750 + 264 = 1014 \, m^2$.

$A$ plot,in the shape of a quadrilateral $XYZW$,has $XY = 25 \, m$,$YZ = 60 \, m$,$ZW = 33 \, m$,$WX = 34 \, m$,and $XZ = 65 \, m$. Find its area. (in $, m^2$)

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