Question

Question 3 mathematics

Answer 1

Part a) The area of the shaded region is
`41\ ft^(2)`

Part b) The area of the nonshaded region is
`87\ ft^(2)`

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=(1)/(2)[(8-2)+3)](8+2) -2^(2) \\ \\A=(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)`