Answer:
The area of the composite figure is 392.12[tex]cm^{2}[/tex].
Step-by-step explanation:
The area of the composite figure = area of trapezoid + area of rectangle
Area of trapezium = [tex]\frac{1}{2}[/tex] ( a +b)h
Where: a is the length of the first base, b the length of the second base and h is the height of the trapzium.
Applying Pythagoras theorem, the height, h, is;
h = [tex]\sqrt{5^{2} - 1^{2} }[/tex]
= [tex]\sqrt{24}[/tex]
h = 2[tex]\sqrt{6}[/tex]
Area of trapezium = [tex]\frac{1}{2}[/tex] ( a +b)h
= [tex]\frac{1}{2}[/tex] (13 + 12) × 2[tex]\sqrt{6}[/tex]
= 156[tex]\sqrt{6}[/tex]
= 382.12[tex]cm^{2}[/tex]
Area of trapezium is 382.12[tex]cm^{2}[/tex]
Area of rectangle = length × width
= 5 × 2
= 10 [tex]cm^{2}[/tex]
Area of rectangle = 10 [tex]cm^{2}[/tex]
Therefore,
area of the composite figure = 382.12 + 10
= 392.12[tex]cm^{2}[/tex]
