Answer:
Area of given figure is 216 mm².
Step-by-step explanation:
Area of the given figure = Area of triangle + Area of Rectangle
Area of triangle whose sides are known is determined by the formula:
[tex]Area = \sqrt{s(s-a) (s-b)(s-c)}[/tex]
where s is the semi-perimeter of the triangle. i.e.
s = (a + b + c) ÷ 2
⇒ s = ( 12 + 16 + 20) ÷ 2 = 24 mm
Then [tex]Area = \sqrt{24(24-12) (24-16)(24-20)}[/tex]
⇒ [tex]Area = \sqrt{24\times12\times8\times4}[/tex]
⇒ Area = 96 mm²
Area of Rectangle = length × width
Area = 6 × 20 = 120 mm²
∴ Total Area = 96 mm + 120 mm = 216 mm²
Thus, Area of given figure is 216 mm².
