Answer:
[tex]150cm^2[/tex]
Step-by-step explanation:
[tex]area =[/tex] [tex]\frac{1}{2} * 12 * (y + x + y + z)[/tex]
[tex]area =[/tex] [tex]6 * (x + 2y + z)[/tex]
[tex](y + z)^2 + 12^2 = 20^2[/tex] [tex]and[/tex] [tex](x + y)^2 + 12^2 = 15^2[/tex]
[tex](y + z) =[/tex] [tex]\sqrt{20^2-12^2}[/tex]
−−−−−−−− [tex]= 16cm[/tex]
[tex](x + y) =[/tex] [tex]\sqrt{15^2-12^2}[/tex]
−−−−−−−− [tex]= 9cm[/tex]
[tex]area =[/tex] [tex]\frac{1}{2} * 12 * (\sqrt{20^2-12^2} + \sqrt{15^2-12^2})[/tex]
[tex]area = \\[/tex] [tex]6 * (16+9)[/tex]
[tex]area = 150cm^2[/tex]
Pythagorean Theorem
We can apply this by breaking down the trapezoid in two triangles.
[tex]base =[/tex] [tex]\sqrt{(20^2 - 12^2}) + \sqrt{(15^2 - 12^2)[/tex]
[tex]base =[/tex] [tex]25[/tex]
[tex]area =[/tex] [tex]\frac{1}{2}bh[/tex]
[tex]area =[/tex] [tex]\frac{1}{2} * 25 * 12[/tex]
[tex]area =[/tex] [tex]150cm^2[/tex]
