Question

Question 3 mathematics

Answer 1

Answer:

Part a) The area of the shaded region is $41\ ft^{2}$

Part b) The area of the nonshaded region is $87\ ft^{2}$

Step-by-step explanation:

we know that

The total area is equal to the area of the shaded region plus the area of the nonshaded region

step 1

Find the total area  

The total area is equal to the area of the rectangle

$A=8(16)=128\ ft^{2}$

step 2

Find the area of the shaded region

The area of the shaded region is equal to the area of the  trapezoid minus the area of the smaller square

so

$A=\frac{1}{2}[(8-2)+3)](8+2) -2^{2} \\ \\A=\frac{1}{2}[9](10) -4\\ \\A=41\ ft^{2}$

step 3

Find the area of the nonshaded region

The area of the nonshaded region is equal to the total area minus the area of the shaded region

so

$A=128\ ft^{2}-41\ ft^{2}=87\ ft^{2}$