Find the area and perimeter of ABC at right. Give approximate (decimal) answers, not exact answers

Answer:Area of Δ ABC = 21.86 units squarePerimeter of Δ ABC = 24.59 unitsStep-by-step explanation:Given:In Δ ABC∠A=45°∠C=30°Height of triangle = 4 units.To find area and perimeter of triangle we need to find the sides of the triangle.Naming the end point of altitude as 'D'Given [tex]BD\perp AC[/tex]For Δ ABDSince its a right triangle with one angle 45°, it means it is a special 45-45-90 triangle.The sides of 45-45-90 triangle is given as:Leg1 [tex]=x[/tex]Leg2 [tex]=x[/tex]Hypotenuse [tex]=x\sqrt2[/tex]where [tex]x[/tex] is any positive numberWe are given BD(Leg 1)=4∴ AD(Leg2)=4∴ AB (hypotenuse) [tex]=4\sqrt2=5.66 [/tex]  For Δ CBDSince its a right triangle with one angle 30°, it means it is a special 30-60-90 triangle.The sides of 30-60-90 triangle is given as:Leg1(side opposite 30° angle) [tex]=x[/tex]Leg2(side opposite 60° angle) [tex]=x\sqrt3[/tex]Hypotenuse [tex]=2x[/tex]where [tex]x[/tex] is any positive numberWe are given BD(Leg 1)=4∴ CD(Leg2) [tex]=4\sqrt3=6.93[/tex]∴ BC (hypotenuse) [tex]=2\times 4=8 [/tex]  Length of side AC is given as sum of segments AD and CD[tex]AC=AD+CD=4+6.93=10.93[/tex]Perimeter of Δ ABC= Sum of sides of triangle⇒ AB+BC+AC⇒ [tex]5.66+8+10.93[/tex]⇒ [tex]24.59[/tex] unitsArea of Δ ABC = [tex]\frac{1}{2}\times base\times height[/tex]⇒  [tex]\frac{1}{2}\times 10.93\times 4[/tex]⇒ [tex]21.86[/tex] units square