someone please explain to me how to find the area PLEASE! Find the area and perimeter of quadrilateral ABCD below. Explain your process for finding both the area and the perimeter, and show your mathematical steps clearly.

Accepted Solution

Answer:Part A) The area of the figure is [tex]24\ units^{2}[/tex]Part B) The perimeter of the figure is [tex]20\ units[/tex]Step-by-step explanation:step 1Find the area of the figurewe know thatThe area of the figure is equal to the area of triangle ABD plus the area of triangle BCDThe area of triangle is equal to[tex]A=\frac{1}{2}bh[/tex]Area of triangle ABDObserving the graph[tex]b=BD=(-2+8)=6\ units[/tex][tex]h=(9-5)=4\ units[/tex]substitute[tex]A=\frac{1}{2}(6)(4)=12\ units^{2}[/tex]Area of triangle BCDObserving the graph[tex]b=BD=(-2+8)=6\ units[/tex][tex]h=(5-1)=4\ units[/tex]substitute[tex]A=\frac{1}{2}(6)(4)=12\ units^{2}[/tex]The area of the figure is[tex]12\ units^{2}+12\ units^{2}=24\ units^{2}[/tex]step 2Find the perimeter of the figurewe know thatThe perimeter of the figure is equal to[tex]P=AB+BC+CD+AD[/tex]we have[tex]A(-5,1),B(-8,5),C(-5,9),D(-2,5)[/tex]the formula to calculate the distance between two points is equal to [tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex] Find the distance AB[tex]d=\sqrt{(5-1)^{2}+(-8+5)^{2}}=5\ units[/tex] Find the distance BC[tex]d=\sqrt{(9-5)^{2}+(-5+8)^{2}}=5\ units[/tex] Find the distance CD[tex]d=\sqrt{(5-9)^{2}+(-2+5)^{2}}=5\ units[/tex] Find the distance AD[tex]d=\sqrt{(5-1)^{2}+(-2+5)^{2}}=5\ units[/tex] substitute the values[tex]P=5+5+5+5=20\ units[/tex]