what is the area of the composite figure if line AB is congruent to line BC which is congruent to line CD which is congruent to line DA which is congruent to DN? (2pi+28)mm^2
(2pi+32)mm^2
(2pi+40)mm^2
(2pi+48)mm^2

(2pi + 40)mm²

Step-by-step explanation:

semi circle = 1/2 pi (2)²

2 squares = 2 * 4 * 4 = 32

2 triangles = 2 * 1/2 * 2 * 4 = 8

Work Shown:

Segments AB, BC, CD, DA, and DN are all the same length (4 units)

The semicircle has area of

A = (1/2)*pi*(radius)^2

A = 0.5*pi*2^2

A = 2pi

The square has area of

B = (side length)^2

B = 4^2

B = 16

The trapezoid has area of

C = (height)*(base1+base2)/2

C = (DN)*(CD+MK)/2

C = (4)*(4+8)/2

C = 24

Add up the results of A, B and C to get the total area

A+B+C = 2pi+16+24 = 2pi+40

The total area is 2pi+40 square mm

7

step-by-step explanation: