Answer:
[tex]\huge \boxed{\mathrm{36\sqrt{3} +72 \ mm^2}}[/tex]
Step-by-step explanation:
The height of the triangle is important to find the area of the rectangle.
We can split the triangle in half, we get a right triangle.
Apply Pythagorean theorem to solve for the height.
3² + b² = 6²
b² = 6² - 3²
b² = 36 - 9
b² = 27
[tex]b= 3\sqrt{3}[/tex]
The length of the rectangle is 3 + 3 + 3 + 3 = 12 mm
The width is 3 + [tex]3\sqrt{3}[/tex] + 3 = [tex]3\sqrt{3}+6[/tex] mm
The area of a rectangle is length × width.
[tex]12(3\sqrt{3}+6)[/tex]
Distribute.
[tex]36\sqrt{3} +72[/tex]
The area of the rectangle is [tex]36\sqrt{3} +72[/tex] mm².
