Question

A trapezoid, square, and semicircle are connected to form a composite figure. Trapezoid M D C K has base lengths of 8 millimeters and 4 millimeters. Square A B C D has side lengths of 2 millimeters. Line A B is the diameter of the semicircle and has a length of 4 millimeters. What is the area of the composite figure if AB ≅ BC ≅ CD ≅ DA ≅ DN? (2π + 28) mm2 (2π + 32) mm2 (2π + 40) mm2 (2π + 48) mm2

Answer 1

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