Answer:
(2π + 28) mm²
Step-by-step explanation:
The Area of the Composite figure =
Area of the Trapezoid + Area of the Square + Area of the semicircle
a) Area of the Trapezoid
Trapezoid M D C K has base lengths of 8 millimeters and 4 millimeters
Diameter of the semicircle= length of 4 millimeters = height of the trapezoid
Area of trapezoid = 1/2 × h × (b + b)
= 1/2 × 4 × (8 + 4)
= 1/2 × 4 × 12
= 1/2× 48
= 24mm²
b) Area of the square
Square A B C D has side lengths of 2 millimeters.
Area of a square = Side length²
=(2mm)² = 4mm²
c) Area of the semicircle
Line A B is the diameter of the semicircle and has a length of 4 millimeters.
Formula for the Area of a semi circle: πr²/2
Radius = Diameter/2 = 4mm/2 = 2mm
= π × 2²/2
= 4π/2
= 2πmm²
The Area of the Composite figure =
Area of the Trapezoid + Area of the Square + Area of the semicircle
= 24mm² + 4mm² + 2πmm²
= 28mm² + 2πmm²
= (28 + 2π)mm²
Therefore, the Area of the Composite figure = (28 + 2π)mm² or (2π + 28) mm²
