Answer:
(52 +32π) mm² ≈ 152.5 mm²
Step-by-step explanation:
The idea with these composite shapes is to divide them into parts whose area formulas you know.
This shape can be divided into two rectangles and a semicircle. The relevant area formulas are ...
Semicircle Area = 1/2πr² . . . . . r is the radius
Rectangle Area = LW . . . . . . . . L and W are the length and width
__
The area of the semicircle with radius 8 mm is ...
Semicircle Area = 1/2π(8 mm)² = 32π mm²
The area of the rectangle at left is ...
Left Rectangle Area = (6 mm)(2 mm) = 12 mm²
The area of the rectangle at right is ...
Right Rectangle Area = (8 mm)(5 mm) = 40 mm²
__
The total figure area is ...
Figure Area = Semicircle Area + Left Rectangle Area + Right Rectangle Area
Figure Area = 32π mm² +12 mm² +40 mm²
Figure Area = (52 +32π) mm² ≈ 152.5 mm²
