Part A: the area of a square is (9a^2 - 24a +16) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work

Length of each side of the square=3a-4

Step-by-step explanation:

Given

Area of a square is =(9a^2 - 24a +16)

Factorising

(3a)^2 - {3*4(2a)} + 4^2

(3a-4)^2

Area of a square =length^2

(3a-4)^2 =length^2

Square root both sides

√(3a-4)^2 = √length^2

3a-4=length

Length of each side of the square=3a-4

Check:

(3a-4)^2

=(3a-4)(3a-4)

=9a^2-12a-12a+16

=9a^2 - 24a + 16

189.3cm^2

Step-by-step explanation:

Find the area of the rectangle first (10 x 15) = 150

Then find the area of the semi circle using pi (3.142 x 5^2) = 78.55/2 = 39.275

Then just add them together 150 + 39.275 = 189.275 to 1 d.p = 189.3

Area of the shape = 189.3cm^2